Bitcoin wallets are where your store your Bitcoins. When you send Bitcoins, the Bitcoin leaves your wallet and goes to another wallet. A Bitcoin can only be in one wallet at a time. Bitcoin wallets are generally free or come with simple registration. You can have multiple Bitcoin wallets and move all or some of your Bitcoins to various wallets. To send Bitcoins to a wallet, you enter the destination wallet ‘address’ (which is a long series of letters and digits) and the amount of Bitcoin that you want to send.
When you submit the request your Bitcoin transfer is automatically processed and verified by the computers that are mining for Bitcoins. With Bitcoins, the wallet to hold the Bitcoins and way to processing payment with Bitcoins is almost free. You can have both offline Bitcoin wallets and online Bitcoin wallets.
Online Bitcoin wallets are often the easiest way to start. Probably the best and easiest way to get started with a bitcoin wallet is with Coinbase.
If you want a offline wallet, start by downloading your free offline Bitcoin wallet. This wallet will remain on your computer and will not be available through a website unless you access your computer remotely with a program like Logmein. It is best practice to backup your offline Bitcoin wallet with another offline backup (or two) as well as an encrypted online service like dropbox, carbonite etc.