It's importantant to make a BACKUP and store it safe.
Bitcoin wallet is a file containing private keys and corresponding public keys (bitcoin address). You can have a lot of wallets (better to have them protected by strong password) and every wallet can control multiple private keys (and addresses). Every address can be considered as private acount number.
Three basic types of wallets:
- Web - Very quick setup, bitcoins kept by third party you have to trust them. (registration required, e-mail or usually phone)
- Desktop ( download and install a client )
-Full client: require to download the blockchain - takes few days to synchronize (check bootstrap to make it faster)
-Lightweight: synchronized and ready to use in few minutes (RECOMMENDED FOR BEGINNERS)
- Hardware ( most secure )
Check actual wallet overview at bitcoin.org