A bumper (also known as a bump or eyecatch) is a static image or short video that usually marks the transition between a program and a commercial break. Usually the name or logo of the program will be displayed, sometimes accompanied by the announcement that the program will return "right after these messages."
Bumpers were developed for children's television in order to clearly dilineate between the show and the paid commercials, since it was believed that children may not be able to discern the difference. The practice has become standard for many programs since then.
Many Japanese anime programs utilize bumpers, referring to them as eyecatches instead. Presumably this is because they draw the viewer's attention back to the screen at the end of a commercial break.
Adult Swim is famous for its bumpers, which they refer to as bumps. Their bumps consist of simple (usually) white text on a black background. Unlike other programs' bumpers, the content of these bumps changes regularly to reflect various happenings at the studio.