A Destroyer is a class of warship smaller than a Cruiser but larger than a Frigate. They are generally used as escorts for convoys or larger warships, or as system pickets patroling the lesser-traveled parts of a solar system on the lookout for smugglers, pirates, unauthorized asteroid miners, and enemy ships on infiltration or recon missions.
Too small to be equiped with a gravity drive, they generally carry no starfighters and only a handful of other small craft, and have very small Marine detachments and no options for landing them on a planet surface other than one or two assault pinnaces. Many older destroyers do not even have artificial gravity on board, and thus operate in a zero-g environment unless actively maneuvering, and are limited in their top acceleration by the physical frailty of the crew (2-3 G's sustained acceleration, 6 G's in brief spurts).
Destroyers, like so many other warship classes, were the brainchild of Jackie Fisher. Originally called Torpedo Boat Destroyers, that was their main job: destroy enemy torpedo boats before they could sink your own Battleships. Later, they also became important as antisubmarine vessels, radar pickets, and general escorts for convoys and larger ships. In space, they continue their role as generalized escort and patrol vessels.