In standard fantasy and magical a terms a cantrip is any spell of very low power (or minor effect). They may look cool, but they accomplish very little.

Cantrips are usually the first spells that a young fledgling wizard will learn. Little things like making a flame dance over your hand, or blowing all the dust out of a room. A cantrip can clean your toilet, cook an egg, or fill your mug with ale, but it certainly can't hold off the marauding hordes of Troglodytes.

Cantrips are mostly a tool of education, you don't want to teach your apprentice how to toss a fireball right off the bat, thats a good way to get your house burned down. Instead you teach them how to refill the cat's food dish with magic. An apprentice wizard will probably learn hundreds of cantrips before they ever conjure up their first magic missile.

Different game systems deal with the cantrip in different ways. They are non existant in the original Dungeons & Dragons game. The first edition of Advanced Dungeons & Dragons had a hundred or so of them listed (in the Unearthed Arcana rulebook), where you could memorize four cantrips in lieu of a first level spell. Second edition AD&D reduced the cantrip to a single first level spell that can have akmost any minor effect (I have no idea what the third edition rules did to cantrips). Other games may allow wizards to use as many cantrips as they like, as is often the case in fantasy fiction (those archmages seem to be able to toss little spells around all day long, with no signs of tiring). Other games (like Changeling the Dreaming), have changed the meaning of the word, and have a whole different idea of what the cantrip is.

When you get right down to it, the cantrip is a magic trick, done with real magic, instead of just sleight of hand. This is one of the reasons that so many failed wizards apprentices become street magicians. Their magic has no other use than minor amusement or trickery (not to mention that a magic card trick always works).

Tiefling says 3rd Edition D&D is back to the '0-level cantrip list' system, but they're not quite as inane as the Unearthed Arcana system. There's a heal-one-point spell (actually a cleric cantrip, or orison), there's 'Ray of Frost' - roll to hit, 1d3 points of damage