Google sells things. A lot of things. And for what seems like forever now it's given you a first-party way to pay for them. We once used Google Checkout, which traditionally was used for online payments from a traditional computer. But that's come and gone, and now we have Google Wallet.
Google Wallet itself was born from the idea that it should be easy to pay for things with your phone. Wallet had a pretty rocky beginning, though, as few creditors and even fewer mobile carriers were on board. (Google Wallet competitor ISIS attracted much of their attention. It hasn't done too hot either, though.) Rather than have one mobile payment system and another for everything else, though, Google Checkout morphed into Wallet, and it's all now neatly tied into your Google account.
Want to buy an app? A book? Music? Movie? TV show? You use Google Wallet. Want to pay for something in an online store? You can use your Google Wallet account. It's easy (if you've used Paypal, you get the gist already), and it's got Google behind it.
Google Wallet also lets you sent money directly to individuals with their own Wallet accounts, and you can use it as as a repository for your loyalty cards as well.