Conflict, theme, and moral are all connected via the motif presented in a work – for this reason, a successful motif or set of motifs are required to ensure a theme isn't lost and the story's moral is highlighted.
Motif foundation: conflict and theme
Let's talk conflict for a second. Theme is often thought of in terms of opposed binaries such as: "good vs. evil" or "man vs. machine". These, however, are sources of conflict rather than properly developed themes. They motivate an author to write a wonderful story, but there is more to a theme than just a conflict.
Themes make a claim related to the central conflict. I tell my students that the theme of Tolkien's The Lord of the Rings is not just "good vs. evil" but rather "a small good can counterbalance or undo a great evil." By adding this layer of specificity to a conflict, a writer can usefully narrow, empower, and develop the theme of their story. It is more satisfying, and much more important that we understand the theme of the story, than that we understand the conflict. The theme leads us toward the moral in a way that a statement of the conflict does not. Saying "the story is about society versus machine" does not tell us anything about who should be favored in the conflict; the claim "society is improved by the presence of machines" is a more powerful theme because it indicates a possible moral.
A good moral is supported by motif and theme
Our moral is one step removed from the theme. The moral of The Lord of the Rings relates more to companionship, than to good and evil, for instance. Sticking beside one's friends is the source of the hero's success: their connections are what give them the strength to remain good and act as a counterbalance to evil, not their individual power. A theme engages us with a question, but the moral provides the answer. Good stories tend to have a theme and a motif which support the moral.
Motif
To the subject at hand: a motif is a recurring pattern, set of symbols, or set of ideas which help to illustrate the theme. Once you've nailed down your theme, the motif or motifs of your story are the recurring elements which support that theme and demonstrate to your reader the persistence of the theme. It is important that motifs are a recurring element of the story because persistence or repetition illustrates that an element of a fictional narrative is intended to be a representation of something true. Let's discuss that more simply.
A motif is formed when a conflict is represented to have resolved in the same manner, repeatedly. Basically, a motif is a collection of moments that reinforce a theme – but it must be a collection of moments, it cannot be a one-off example. When Boromir gives his life for the hobbits; when Sam goes with Frodo to Mordor; and when Smeagol journeys with Sam and Frodo, these events each collectively form a motif which describes the theme of companionship. Independently these events may be dismissed by the reader as necessary for the narrative, or simply an element of literary worldbuilding. Taken together they undeniably indicate a larger meaning and lead the reader to seek a moral. In Tolkien's case each example of companionship is meant to lead toward the realization that "good triumphs through friendship."
Elements of a motif
Motifs can be created by connecting a number of elements. Above I have described a variety of events – plot points – which form a motif, but symbols can do the work of creating a motif as well. So long as those symbols are reiterated and tied back to the theme, they can be used as elements of a motif. For instance, Wonder Woman's lasso is a powerful symbol for truth, and its use is reiterated across her adventures: an item may be a one-off symbol, but when symbols are repeatedly tied to a particular outcome, they create a motif. The "lasso of truth," as well as the "one ring" are excellent examples of a symbol which is foundational to a motif. Further, there is no requirement that a motif be constructed using only one literary tool: the burden of the ring is a powerful symbol, but of course it is connected to characters and plot events, and all of these (the symbol, the characters, and the plot events) form a motif.
Sometimes the motif has a particular value in-and-of itself. Readers don't judge a motif just on what it portrays, but also in how it portrays it. For instance: why a ring? Why not a sword or a pendant? We can speak to the value of the symbol: a ring is something that we can choose to wear, just as we must choose to be "good"; but readers can also understand the motif as it appears to them outside of the context of the theme, the moral, and the conflict. For instance, the motif in The Lord of the Rings tends to focus on small things: small people, small items, and small moments in time. Often the theme and the motif will share a number of qualities, but this is not always the case: we can and often do think of motifs as distinct from the theme which they reinforce.
To clarify, consider a common set of symbols or events: blood; the death of a husband; and the gaining of an inheritance. All of these may form a coherent motif – they seem connected metaphorically – but they might describe any number of disparate themes. The theme could be one of seeking vengeance, one of tragedy, or even one of redemption. Similarly, motif is distinct from moral or conflict. Given the motif above, we cannot determine the central conflict or the moral which is intended in this hypothetical work. Certain genres tend to use motifs which rely on elements related to those genres, and there are expectations associated with each motif: a "gothic motif" for instance will use "blood" differently than a story with a "mystery motif" – in the first blood is an element of horror and in the latter, it is a clue. Regardless of our assumptions we cannot make a strong guess at what a motif means until some of the elements of that motif are clearly defined in relation to the theme.
So, how can we best use a motif? In my opinion, a motif is best used to join seemingly unrelated elements of fiction such that a web of associations is formed – each symbol, each individual event, or each character trait thus contributes to the power of other symbols, other events, and other moments of character development. Take for instance these elements of a motif: "The ring is a burden;" "men are corruptible;" "small things are powerful." None of these elements need necessarily be related. A story could be told about any one of these things, but through their relationship in The Lord of the Rings, each element of the story is magnified. Due to the fact that "the ring is a burden" we know that those small folks who carry it are powerful; and due to the fact that "men are corruptible" we know that "the ring is a burden" because it is what causes the corruption. There is a sort of feedback loop formed where relationships between symbols, events, and character traits mean that each additional detail increases the value of previously established details: this is a motif.
Theme in motif
Finally, a motif itself might have a theme. Perhaps a motif of violence which uses the symbol of a knife, the death of a queen, and a character who is a serial killer. Some of the best motifs utilize metaphorically coherent symbols: consider the use of the disease and poison motif in Shakespeare's Hamlet: Something is rotten in the state of Denmark.
Or changes of body in Stoker's Dracula: aging, failing to age, loss of health, illness, and blood are all deeply related on a metaphorical level even before Stoker begins to form connections between these narrative elements.
A good motif will make use of the connections or lack of connections between the elements of that motif, either to emphasize the relationships between elements of a motif, or to emphasize a distinction of one element amongst many. Consider what type of story you are telling, and reveal connections between the elements of the motif accordingly: consider taking your time in connecting elements to create or maintain tension: how is the ring related to darkness? We don't discover the connection until Frodo has already evaded the Ringwraiths. Or consider connecting elements of a motif more quickly to increase the pace of a work or in an initiating event: drawing the sword from the stone and becoming king are both elements of an Arthurian motif connected to the theme of "seizing one's destiny." The connection between the sword and the divine right of kings is established quickly to garner the reader's attention.
Do not get hung up on creating a motif, but to be aware of it once you have started writing. Look back on your work, and tweak elements of your motif to better create the feedback loop I have described above. Change a symbol, alter a character trait, or add or remove an event in your story to better support your motif.
A few examples of the relationship between motif and theme
Let's take a quick look at ten examples of motifs and the themes they support:
Frankenstein by Mary Shelley
Motif: "The doppelganger." Characters who look similar but with variation which makes them seem unnatural.
Theme: "Who is the real monster?"
To Kill a Mockingbird by Harper Lee
Motif: "Village/Rural." Characters who mind the business of others.
Theme: "Persecution is a result of mob mentality and seeing people as different from the group you feel you belong to."
Anna Karenina by Leo Tolstoy
Motif: "Forgiveness." Especially Christian forgiveness.
Theme: "Let bygones be bygones and every family is sad in their own way."
Harry Potter by J.K. Rowling
Motif: "Abuse of Authority." Professorship, political power, house elves, etc...
Theme: "It is not the power we possess, but how we wield it."
Spider-Man by Marvel
Motif: "Commitments." Homework, superheroing, relationships! How can one teenager manage it all?
Theme: "With great power comes great responsibility."
1984 by George Orwell
Motif: "Thought/Emotion Control." The Party's power, Big Brother's watching eye, and children spying on their parents.
Theme: "Totalitarianism, once entrenched, cannot be easily resisted."
Don Quixote by Miguel de Cervantes
Motif: "Chivalry/Honor." Old Don picking fights with windmills and everyone else to show that he is a worthy man.
Theme: "One's (social or economic) class is not the same as one's worth."
Jane Eyre by Charlotte Brontë
Motif: "Fire." The fire in the red room, when Jane saves Mr. Rochester, when Thornfield burns to the ground.
Theme: "The complexities of self-sacrifice: when to love and when to live."
Hamlet by William Shakespeare
Motif: "Ears and Hearing." Spying, overhearing confessions, poison in the ear.
Theme: "The complexity of taking action: what do we know, and can we ever know enough to act on that knowledge?"
The Brothers Karamazov by Fyodor Dostoevsky
Motif: "Children and their differences." The brothers themselves, their father and father figures.
Theme: "For what are we morally responsible, and who determines our morale responsibilities?"