Every piece of literature explores a theme. It is usually easy to recognize - the author wants you to feel and understand the theme, after all. In fact, there may be multiple themes for you to appreciate in one piece of literature. The difficulty arises when we try to give name to the themes we explore. This is because themes are big ideas, ideas which are hard to put precicely into words.
What is love? What is justice? What is victory? The words fail to encapsulate their meanings, yet when we add more to their description, it feels that we merely fall further from the mark. That is because these things are not things. They are relations, which exist between things in the material world. Though our words are very good at representing material things and actions, they struggle to adequately describe relations to the fullest extent of their significance. This is precisely why the bulk of literature exists. There may be no better way to describe these immaterials, than in a novel in which characters grapple with their effects or with the concepts themselves.
Traditionally, when we identify a theme in literature studies, we use a complete sentence to represent it (even with the difficulties mentioned above). For example, we would say that the theme of story X is, "Love can make you blind", rather than just, "Love". The reason why we do this has more to do with the requirements of academia, than with conceptual accuracy.
The term, motif actually comes from classical music. There, it refers to a small piece of melody that recurrs within a larger work or composition, and used to convey significance, leading the audience's attention to the thematic content. Think of the opening to Beethoven's 5th symphony (you know it - Dun dun dun DUUUN). Deep and brooding, this sequence of notes is repeated throughout the work, and conveys the feelings and ideas which Beethoven wished to explore.
A motif works the same way in literature. Instead of a repeated melody, it might be a repeated image or event. It's the pattern you notice that helps develop the central theme. It cues you to focus your thinking on the concepts the author wishes for you to explore.
The Lottery by Shirley Jackson can be hard to read, not in terms of lexical difficulty, but in its sheer brutality. As you read, pay attention to the patterns you notice. Slips, stones, the box... every element of the tradition serves its purpose, as the central ritual of the lottery itself is the motif. Try to identify what you consider to be its main theme with one complete sentence.
Marigolds by Eugenia Collier is a poignant coming-of-age story set in rural Maryland during the great depression. Try to identify the themes expressed in this narrative using complete sentences. Then, identify at least one motif.
Back to literary terms.