Back at the end of May during Google's annual developer conference, Google confirmed that they would be introducing a buy button that would make it easier for users to purchase products, only at the time it wasn't stated when exactly Google would be launching the buy button within their search results as it was only mentioned that it was coming soon. Prior to the confirmation it had been speculated on for a couple of weeks. Alongside the lack of an actual date for the launch of this service, Google was light on other specific details like what the service would be called. Google has officially unveiled the new service as of this morning and it will be called Purchases on Google which seems appropriate and to the point since that's where users will see the buy button.
Those who see these mobile search ads with a buy button will not actually make their purchases through Google, rather Google will simply be hosting the ad with a buy button for a specific product, and should users click the button to make a purchase they'll actually be taken to the manufacturers website to complete the transaction. For Google, this is just a way for them to "reduce some of the friction" between the user and the ad click on mobile searches, which basically means they're trying to introduce a way for users to be more inclined to click on ads to buy products.
Google mentions that they don't want to dilute the relationship between the buyer and the seller, which explains why they won't be selling the products themselves. As for what products users will see these buy buttons with when they search for things, at the moment Google is only testing the buy button. Google has stated that they are working with a small number of companies right now (and for the next few weeks) to test out 'Purchases on Google', with more companies being added into the mix at a later point. Google plans to roll out the feature to more advertisers will span throughout the rest of this year and continue into next year and will be in the U.S. only for now.