The free card play is often made in hold'em and means one invests and extra bet on a cheap street (like the flop) in order to get a free card on the expensive streets (usually the turn).
There is a common tendency in hold'em for players to "check to the raiser." It's often right to check to the raiser, but this tendency allows for the "free card play." Basically the free card play is setup on the flop when the bets are small with a late position player raising. On the turn the "check to the raiser" behavior kicks in and everyone checks to the player who raised on the flop. Now, that raising player has a choice; she can bet or, if on a draw, she can elect to check and take a free card. If she takes the free card, she paid a small bet on the flop (the raise) to get to see the river card for free.
The free card play is a powerful tool for players on a draw. Of course, if you have a made hand and there are draws on board, it's best to thwart the free card play by betting into the raiser in an attempt to take away the pot odds for her draw.