Damage over Time. Instead of all the damage from a power applying right when the power hits, the damage accumulates over time. For instance, setting something on fire will not cause the object to instantaneously incinerate, but usually has lingering flames that cause additional damage. The use of DoT in most gun and rifle attack powers is that multiple projectiles are hitting the target.
Note: Since the introduction of "one-shot protection" which prevents a single attack killing a player on full hit points, any suitably devastating DoT attack can get around this restriction - losing 99% of your Hit Points in the initial damage, with a DoT component thereafter, killing you the next time damage is applied - often in less than a second.