Catapults are medieval weapons used as siege engines to cause damage to outer walls of buildings. The device is to be loaded with large ammunition (such as a boulder or cannonball, amongst other things). Tension is then created by pulling back the catapult and tightening a rope (or by using a counterweight). The seat on the catapult is then released, throwing the ammunition towards its intended target. The stored energy in the catapult is capable of providing great momentum for the projectile.
Amy Rose and Tekno the Canary discovered a catapult in a 5000AD museum. With power down throughout the whole city, the heroes used the ancient device to defeat culprit Gremlyn. Presumably preloaded with a massive boulder, the girls fired the rock at Gremlyn and defeated the robot.
Catapults have also found more unorthodox uses in Sonic the Comic. In Grounded, Tails was attempting to pull back a palm tree in the Aquatic Ruin Zone so that he could swat a Spider-Moth out of the sky. Unfortunately, the cable snapped, sending Tails flying through the air and into the Badnik.