A trackball is essentially a different kind of computer mouse. It is a plastic case containing a ball on the top that moves a computer cursor around on the screen. The user can move the ball with their thumb or fingers, and sensors inside the case detect which direction the ball is moving. Unlike a mouse, however, the case doesn't move. The user simply rests a hand on it and uses the thumb to move the ball around. Buttons on the side allow users to click on things on screen.
While the standard mouse has replaced the trackball for the majority of home computer users, a lot of specialized work environments still use trackballs due to their precision. Trackballs are used in a variety of fields, from air-traffic controlling to operating equipment to drafting and design work. They are considered more durable than a mouse and more precise, which is why they are still used in these fields.
Compared to older mice that still used a ball and sensor on the bottom of the device to direct a cursor, trackballs had a definite advantage in that the ball was in contact with the user's hand as opposed to a mouse pad or desk top. The user's hand would always be cleaner, which would drastically cut down on the ball getting dusty or dirty or any other setback that would obstruct the sensor.