Clip analysis is the function of using the extent of one geographic layer to clip the extent of another geographic layer. For example, if you had a land use layer for an entire county that you only wanted information for a particular city, you would use clip analysis to crop the extent of the layer by using the geographic layer of the city. The resulting dataset would be land use for the city of interest.
The video tutorial below demonstrates how to use clip analysis using ArcGIS 9.2. The video is 6:46 minutes long.