En-passant in French means "in passing". When en-passant occurs is when a pawn is on its starting position and another pawn(playing black) is a knights position away from the white pawn. When the white pawn moves up 2 spaces the pawn runs through blacks spot where he can capture. On the next move black can choose to attack the pawn or to ignore it. En-passant can only be played after the immediate move. Black can not play en-passant on the move following that.
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En-passent prevents a pawn from using its initial two-space move to avoid capture from an advancing pawn.
Imagine a white pawn has moved to the 5th rank. The pawn in an adjacent column would open itself to capture if it moved from 7th rank to 6th, but the double move it is allowed to take would place it at the 5th rank, beside the attacker.
The en-passent rule allows the white pawn in the next turn only to capture that pawn as if it were in the 6th rank. The white pawn moves diagonally to the 6th rank of that column and the black pawn is removed and captured.
It is difficult to explain the 'en passant' rule in words. The following web link has got a graphical illustration of 'en passant' rule : http://www.chesskids.com/kids/enpas.htm