A free card is exactly that. It is a card that does not cost a bet to receive. While players might get a free card (or cards) in draw poker if a hand is checked around before the draw, concepts about the free card apply primarily to stud and hold 'em games where there are several rounds of betting.
In general, when you have the best hand, you do not want to give opponents a free card since you are giving them a chance to outdraw you and win the pot. By the same token, when you do not have the best hand, you want to try to get a free card to get a free shot at winning the pot.