Motif

a recurring subject, theme, idea, etc., esp. in a literary, artistic, or musical work.
a distinctive and recurring form, shape, figure, etc., in a design, as in a painting or on wallpaper.
a dominant idea or feature.
--Dictionary.com

Technically, the word "motif" can mean a variety of different things. In trope land, however, a motif is best described by the first definition above; it's something symbolic that keeps turning up in order to reinforce the main theme of the work. Usually, this is a physical item, although a motif may show itself in other ways—such as through dialogue. It may even be a double motif: a pattern on somebody's sofa, an emblem on the heroine's shirt or a bumper sticker on the hero's car.

Sometimes it can be difficult to establish what is a motif, and what isn't. Their defining characteristics are that they appear more than once and they must be significant in some way. A sea shell on its own is not a motif. However, if a painting of a seascape turns up ten minutes later, followed by a tank full of tropical fish, then that sea shell probably is a motif - the objects that show up afterwards reinforce the theme of "the sea."

Broadly speaking, motifs are employed in three different ways:

A single object, or a collection of extremely similar objects, that appear(s) many times throughout the course of the play/film/book. Tends to place a lot of importance on the item itself, possibly at the expense of whatever they are supposed to represent. Example: The titular Glass Menagerie, in particular the glass unicorn.
A collection of related objects or symbols that appear over and over again. Generally the most popular option, as it marks the motifs as significant, but puts the emphasis firmly on the theme. Example: the various vehicles that appear in the Revolutionary Girl Utena movie.
An assortment of objects that don't seem to be related, but on closer inspection have an underlying resemblance that serve the theme. For example, a black cat, spilled salt and an umbrella left open indoors all point to the theme of bad luck. The audience may have to spend some time looking for the connection.

In literature, television or film, it's quite rare, although not impossible, for a motif to be a theme in itself. It's possible that the dead roses the hero and his girlfriend keep coming across are just a reflection on their lack of gardening skills if gardening is a theme of the story. It's more likely, however, that the dead roses signify that their romantic relationship is in trouble.

Motifs are a favorite subject for English essays, and they've been responsible for many an epileptic tree - since anything can be a motif if you squint hard enough (and can find some way of relating it to other objects).

Compare with Central Theme and Shapes and Symbols Tropes

This is the Super-Trope to the following tropes: