Taking a free card is to check back to see the next card for free.
This is something we can usually do when we are in position. It means that when our opponents check to us and we have a weak draw or a middleish hand then we can check behind and keep the pot small and see the river for free i.e. take a free card.
Some aggressive players like check-raising on draws on the flop when they’re out of position because even when their opponent calls the raise the play will usually get a free card on the turn.