Cantrip is the common slang term for any Dominion Action card which offers +1 Action and +1 Card. It is essentially self-replacing (not taking up space in your hand or taking up an action) and will usually offer some side benefit, such as the + Peddler offers or the additional +1 Action of Village.
Cantrips harming the deck
In most cases, cantrips are seen as cards that cannot harm the deck, since you receive a benefit by playing them and doing so does not prevent or delay you from drawing other cards in your deck. There are a few exceptions.
Discard attacks like Militia or Goons which require the player to make a choice of which cards to discard are more powerful against hands containing a few cantrips. This is because the player discarding does not know which cards are going to be drawn by the cantrips, so the chance of making a sub-optimal choice is greater.
Similarly, although cantrips don't "take up space" in your deck on your turn since you can draw right past them, there may be cards you want to have in your hand between turns—Reactions to protect you from an opponent's Attack, Province to block an opponent's Tournament, etc. Filling your deck with cantrips will make it less likely that you have in hand the card you need when it's not your turn. (Cards other than cantrips have this property as well, of course; but it's easier to lose sight of the fact with cantrips since they don't have this property on your turn.)
Like any other Action card, a cantrip can be drawn dead—i.e., drawn by a terminal Action card without sufficient +Actions to be able to play the cantrip after you draw it—and thus can harm a Big Money deck that depends on terminal draw without villages.
Cantrips may also be less useful with draw-up-to-X cards like Library, Watchtower, and Jack of all Trades. Although cantrips do not outright harm the deck in these cases, they under-perform other cards which do not draw cards (and which typically offer more benefits in compensation for the lack of draw).
Other Nicknames for Cantrips
Some players refer to Cantrips as 'invisible' cards, based on them replacing themselves into your hand with no net negatives. Donald X has referred to Cantrips as 'free' cards. 
Disagreement over the definition
Some players have differing views on exactly what cards the term "cantrip" encompasses. Some people require that a cantrip exactly replaces itself (i.e. always draws exactly 1 card), while others call cards which sometimes or always draw 2 or more cards (such as Laboratory) a cantrip. Another point of contention is whether cards which can harm you directly, and/or decrease handsize when played—such as Junk Dealer, whose trashing is not optional—are classed as cantrips.
Examples of Cantrip Cards
These cards typically provide +1 Card, +1 Action, and usually some other effect that does not mandatorily change handsize this turn.
- several villages:
- several Peddler variants
- Pawn—can be a cantrip depending on player choice.
- Great Hall
- Pearl Diver
- Market Square
- Sage—filters the deck top before drawing.
- Ironmonger - can act as a Village, a Laboratory variant, or a Peddler variant depending on which card is revealed.
- Sir Bailey
- Herald - arguably can be considered either a Village or a Laboratory variant.
- Ironworks becomes a cantrip if it is used to gain an Action–Victory card.
- Mystic is a cantrip if you can guess what card is on top of your deck.
These cards provide +1 Card, +1 Action, but mandatorily decrease handsize after they draw.
These cards can increase net handsize, on top of their cantrip effect; i.e., they provide non-terminal draw. (Fringe and optional cases are omitted.)
- Wishing Well
- Scrying Pool—allows filtering of the deck top before drawing.
- Hunting Party
- Stables - requires the discard of a Treasure before drawing