In works of art, a motif is an important and noticeable element or feature that typically appears throughout the work. It can relate to the theme, or it can be the dominant or central idea itself. Concepts like betrayal and forgiveness can be motifs, for example, but so can particular images and sounds, such as trees or bells. Motif is also commonly applied in design, where it typically refers to a single or repeated pattern or color. A piece of fabric might have a floral motif; a room may have a black and white motif.
Motif can also appear in scientific contexts, especially in biochemistry, where it refers to a distinctive molecular sequence or structural element that is usually recurrent.
Leitmotif (also and formerly more commonly spelled leitmotiv) has its origins in opera, and is especially associated with Wagnerian opera. The word is from the German words leit and Motif, which translate respectively as "leading" and "motive." In opera, a leitmotif is a recurring melody that accompanies the reappearance of an idea, person, or situation. The term is now applied in other kinds of music, sometimes with a meaning very close to the original: "The Imperial March" that is heard in the Star Wars film franchise whenever Darth Vader appears on screen, for example, is a modern example of leitmotif.
Leitmotif also has extended use that treads the same territory as motif. It's not a common word, but when it is applied it often refers to a dominant recurring theme, as when an image consistently used in an artist's works is described as a leitmotif. Note that some people object when leitmotif is modified by a word like main or dominant, on the grounds that since German leit means "leading" the phrase is redundant. English speakers using leitmotif in English, however, may choose to ignore the objection since leit does not mean "leading" in English.