Storyboarding is the technique interaction designers and information architects have adopted from film and animation to specify interaction in user interfaces. Storyboards in interaction design typically show a sequence of key frames that depict when a change in state occurs in the interface. They are often illustrated with a linear, multi-cell diagram, often accompanied by annotations to describe the actions taken by the user, and the responses or behavior of the system.

In Interaction Design

Storyboards were originally conceived at Disney Studios about seventy years ago. They are a sequential series of illustrations or rough sketches, sometimes including captions of events. Storyboards provide a synopsis for a proposed story (or a complex scene) involving its action and characters.

Storyboards transfer well into the world of the user interface. With a storyboard we can present as frames each step in a sequence of user interactions. Viewing the interaction in a story format helps to refine the interaction and provide feedback for user testing.

Source: "Storyboarding Rich Internet Applications with Visio," by Bill Scott. Boxes and Arrows.

In Film

"a sequential series of illustrations, stills, rough sketches and/or captions (sometimes resembling a comic or cartoon strip) of events, as seen through the camera lens, that outline the various shots or provide a synopsis for a proposed film story (or for a complex scene) with its action and characters; the storyboards are displayed in sequence for the purpose of visually mapping out and crafting the various shot divisions and camera movements in an animated or live-action film; a blank storyboard is a piece of paper with rectangles drawn on it to represent the camera frame (for each successive shot); a sophisticated type of preview-storyboard (often shot and edited on video, with a soundtrack) is termed an animatic"

Source: AMC Film Site

See also definitions from Wikipedia.