Bitcoin wallet is a program which allows you to gain access to, send and receive bitcoins. There are two main types of bitcoin wallets: software and web. Software wallets are programs that you download and run on your PC. Thus, they provide you with complete control over your bitcoin "account". A web wallet is hosted on a website of a company which provides bitcoin wallet services. These wallets are easier to set up and use, but you have to rely on the hosting company to provide sufficient security measures, which can sometimes be a dangerous trade-off.
Bitcoin 101: How do I store my Bitcoins?