Sprite

In the context of sprite animation, a sprite can be thought of as any 2D image that either comes from a video game, or is modeled after those. "Image" is the most general concept that fits here, but typically, this refers to pixel art. Throughout this wiki, you may see "asset" instead of "image", though that is a more generic term that can apply to audio, text, etc.

The definition above is loose enough so as to cover graphics in games like Angry Birds, for example (The Spriters Resource seems to agree with the definition laid out here). In this particular example, the fact that they're stored as bitmaps is misleading—they would still count as sprites even if stored in a vector graphics format, at least in this context.

Other uses of the term
Similar to the term "sprite animation", "sprite" may be used to refer to ideas quite different from the one detailed above. In game development, for example, it would typically refer to some hardware-accelerated image display component, usually meant for dynamic purposes—like the player or enemy characters, bullets, special effects—in contrast with a more static component, meant for background imagery. The Wikipedia article on sprites contains more details on the subject.