A rule of chess that many beginning players don't seem to know about is called

En Passant (which means "in passing" in French).

The rule states that when your pawn is on its fifth rank

(that's the fifth horizontal row away from you)

and the other player's pawn is on its original square

(and one file, or vertical row, to the left or right of your pawn),

and your opponent pushes his pawn two squares forward

(putting it beside your pawn), on your next move (and only your next move),

you may capture the pawn as if it had only moved one square forward.

The rule was added shortly after pawns were allowed to make that

initial two-square jump (a long time ago).