An in-game auto-catcher for Pokémon GO – known as the Explorer Gadget – has been gradually rolling out to users, with the US the most recent region to get in on the action.
As covered by One More Catch, the feature technically remains unannounced by Scopely, and it seems the number of Pokémon it can catch and the number of Pokéstops it can spin actually varies for every player, perhaps suggesting that it's still in the testing phase and not finalised.
That said, if you've got it, you should see an icon for it on the right side of the main screen when playing the game. It'll only work when the app itself is suspended, so you won't get any results if you try using it while playing the game.