A Bitcoin wallet is a software program where Bitcoins are stored. To be technically accurate, Bitcoins are not stored anywhere; there is a private key (secret number) for every Bitcoin address that is saved in the Bitcoin wallet of the person who owns the balance. Bitcoin wallets facilitate sending and receiving Bitcoins, and give ownership of the Bitcoin balance to the user. The Bitcoin wallet comes in many forms; desktop, mobile, web, and hardware are the four main types of wallets.
Source: Bitcoin Wallet