En passant is a chess move in which a pawn is captured despite being horizontally adjacent to the capturing pawn (ordinarily a piece or pawn can only be captured when it is diagonally in front of the capturing pawn).  The capturing pawn moves as it normally would for a capture: diagonally forward, into the file of the captured pawn.

A pawn can only be captured en passant on the very next turn after it has made its initial two square advance.  The rule exists to ensure that a pawn cannot avoid capture by an enemy pawn by using its two square move. 

"En passant" comes from the French meaning "in passing," because the pawn is captured in an attempt to pass the enemy pawn, and is captured "in passing".

An example of en passant, would be as follows: if white had a pawn on a5, and black moved its b pawn from b7 to b5, white could capture "en passant" by moving its pawn from a5 to d6.
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