All robots are designed with a purpose in mind, and these purposes can vary greatly. Robots are traditionally used for tasks that would be unsuitable for a human to do, mainly because these tasks are dangerous, or inaccessible to humans. Dangerous tasks like bomb disposal or handling hazardous waste, as well as inaccessible tasks such as interplanetary exploration are all perfectly suited to robots.
To fulfill their purposes, many robots are required to interact with their environment, and the world around them. Sometimes they are required to move or reorient objects from their environments without direct contact by human operators.
The need for object manipulators applies in competition robotics as well. In the typical VEX Robotics Competition students build a robot to play head-to-head matches against other robots. These games traditionally include some sort of game object that robots must manipulate in such a way that they score points.
The above image shows goal and scored game objects from a past VRC game. Red and Blue colored rings were picked up by robots and placed over posts similar to the one above.
The above two images show a blue trough, and the yellow and green sacks that robots picked up and dumped in them.
The above two images show colored balls and barrels, and the cylindrical goals robots dumped them in.