The availability of sending money using your Wallet account isn't a new offering from Google, since it's been possible by using your Gmail account for quite some time now. But streamlining the process within a mobile app does make the process easier for users. Instead of having to remember the finite details of filling out address fields, you can now tap on a couple of buttons within the Wallet app and the money, or your request for cash, is on its way.
The approach is similar to that of the Square Cash app.
Once you've downloaded the updated app and logged into your Google account, you'll find two new buttons just below your profile photo. The process from here is self-explanatory: tap on Send to send money, and Request to, well, request money. Fill in the required fields (an email address and amount) and send it on its way.
Pro tip: You can view your pending requests in the transaction section of the app, and send a gentle reminder about any owed money.