In most versions of Blackjack, when you are dealt a pair (two of the same card), you have the option to split them into two new hands. You are dealt two more cards (one for each new hand) and your bet is doubled. You play each hand normally you get two chances to beat the dealer (or lose).
Generally, you are allowed to hit or double down on a split hand, with the exception of if you have split two Aces, in which case the two hands are often not allowed to consist of more than two cards. In some cases, a Blackjack achieved on a split hand will not count as such, and simply be valued at 21.