Destroyers are larger ships than frigates, but they still mount the same small-sized modules that frigates use. The Tech 1 destroyers are good at killing frigates and at salvaging, while the Tech 2 destroyers, specifically Interdictors, can deploy warp disruption probes (also known as "bubbles"). Bubbles stop everyone from warping.
With numerous highslots and role bonuses to turrets' tracking and optimal ranges, Tech 1 destroyers are designed specifically to destroy frigates.
Destroyer hulls move much more slowly than frigates and have larger signature radii, making them nearly as easy to hit as cruisers. However, their cramped slot arrangements, powergrid and CPU mean that they can't mount cruiser-sized tanks. As a consequence, they are fragile for their size.
These characteristics limit destroyers uses in PvP, but they have niche roles. Their high damage output (for small, cheap ships) makes them popular tools for suicide-ganking weak targets in highsec. They are sometimes used to hunt frigate pilots or to kill a carrier's fighters. In PvE, they are ideal ships for completing Level 1 combat missions very quickly, and with forethought and good piloting they can complete many Level 2 missions (though for newer players a properly-fitted cruiser is probably a more suitable tool).
Most destroyers have the CPU to fit up to six mining lasers, in order to function as an adequate starter mining vessel; while naturally inferior to the majority of dedicated mining ships, a mining laser-fitted destroyer can still serve as an asset to a mining gang when the pilot can fly nothing better. For a new, low-skill player mining in high-sec, these destroyer-miners can stay on-site in the presence of rats if three high-slots are allocated to weapons. Configured this way, they can fill Secure Containers anchored in high-sec for later pickup without additional support.
Finally, destroyers are also superb salvaging ships because of their many highslots. Salvaging destroyers commonly fit a full highslot rack split between equal numbers of Salvagers and Tractor Beams, with a propulsion module and some Cap Rechargers in the midslots, and as many Expanded Cargoholds as possible in the lowslots. Fitted like this, a Tech 1 destroyer is a suitable salvager for missions up to and including Level 3s, or even some Level 4s if the pilot is willing to make multiple trips to and from the nearest station.
Each race has two T1 destroyer class ships.