This is called en passant, and is a legal move. Check the rules on chess.com for more clarification.
What happened here.

En passant (From Wikipedia, the free encyclopedia)
En passant (from French: in passing) is a move in the board game of chess. En passant is a special capture made immediately after a player moves a pawn two squares forward from its starting position, and an opposing pawn could have captured it as if it had moved only one square forward. In this situation, the opposing pawn may capture the pawn as if taking it "as it passes" through the first square. The resulting position is the same as if the pawn had only moved one square forward and the opposing pawn had captured normally. The en passant capture must be done on the very next turn, or the right to do so is lost.[1] Such a move is the only occasion in chess in which a piece captures but does not move to the square of the captured piece (Burgess 2000:463). If an en passant capture is the only legal move available, it must be made. En passant capture is a common theme in chess compositions.
en passant
This rule was added in the 15th century when the rule giving pawns the option of initially moving two squares was introduced. The rationale is so that a pawn cannot pass by another pawn using the two-square move without the risk of it being captured.
The rule:
If a pawn on its original square moves two squares and there is an opposing pawn on its fifth rank on an adjacent file, the opposing pawn may capture it as if it had moved only one square. The conditions are:
* the pawn making the en passant capture must be on its fifth rank
* an opposing pawn on an adjacent file must move two squares from its initial position in a single move
* the pawn can be captured as if it moved only one square
* the capture can only be made at its first opportunity.
What happened in White's 10th move? I'm playing black, his pawn moves illegally and takes my piece without taking it. You can see this game at http://www.chess.com/echess/game.html?id=41477591
It's still going on, and I'm kind of baffled. Any feedback would be nice. Is it an error? do I report it?