Dumbfire (non-guided) missiles do explosive damage. When launched they will follow the HUD crosshairs they impact on the target or are destroyed by collision, weapon fire, or a Point Defence Turret. Dumbfire missiles travel faster and inflict more damage than seeker missiles, and are most effective against the unshielded hulls of ships.
As an alternative to cannons, Missiles can provide huge damage potential if you can keep them on target. They have a relatively low power draw that makes them a popular choice in smaller ships vs large targets where you have a better chance of keeping on target. Despite the higher projectile speed and deadly force of a missile rack in skilled hands, seeker missiles are almost always the preferred choice.