It's called "en passant". One way of looking at it is that if your opponent moves a pawn 2 squares on it's first move, and thereby "skips" the square in which your pawn could capture it, then on your next move you can still capture that pawn as though it had only moved one square. Below is another explanation for this move which you can find, along with diagrams, by clicking "Chess Rules & Basics" under the "Learn" heading at the top of the page.
En Passant
The last rule about pawns is called “en passant,” which is French basically means “in passing”. If a pawn moves out two squares on its first move, and by doing so lands to the side of an opponent’s pawn (effectively jumping past the other pawn’s ability to capture it), that other pawn has the option of capturing the first pawn as it passes by. This special move must be done immediately after the first pawn has moved past, otherwise the option to capture it is no longer available. Click through the example below to better understand this odd, but important rule.
Could someone please thurily explain the fifth rank rule where you can capture a piece with your pawn as you "pass it"!?