Casting the same spell over and over. Usually spells that have low cooldown are spammed. Can also refer to repeated text when chatting.
Directly translated, "spam" means repetition. Chat spam is repeating the same message over and over, flooding the chat (a common tactic of llamas.) Grenade spam is throwing all your grenades at a spot (without priming them) with the intent of killing people who happen to pass by, as opposed to throwing your grenades at a specific target. Spam kills are regarded as cheap. Throwing all your grenades at someone you specifically want to kill (without priming them) is also spamming, but it's not as bad as spamming when you don't know if someone's there or not.
Spam is a computer game phenomenon prevalent in FPS but also strongly present in many other game genres. Generally, it refers to the repeated, rapid use of an item, weapon or unit. Usually, this takes the form of grenade spamming i.e. a player or players throwing a number of grenades into one area.