"Vibrate" is used to call the users attention to certain events, as well as to give "haptic feedback". This includes (but is not restricted to):
- haptic feedback: e.g. to confirm input (having tapped a key on the virtual keyboard and the like)
- notifications: e.g. vibrate on incoming calls/messages etc., or on other events happening. This can be in addition to a sound played -- or, especially useful, if you've put your device into "silent mode" to not disturb other people, to not miss a notification though no sound is played.
Other uses are thinkable (if not even yet practiced), such as haptic feedback in games (imagine a car race, you're the driver, and you speed up your car/bike and have it "roar" not only by sound but by feeling as well).