Swiping that picture will often net you a handful of items, like some Poké Balls or a Pokémon Egg that, when hatched, could add a new Pokémon to your collection.
There are various power-up items you can purchase for your Pokémon to increase its combat power.
There are medals you can earn for completing certain achievements, like catching a number of Pokémon of a certain type, or walking a set distance.
Other than having something to brag about, though, these medals don't offer you much.
You do need to have a stable online connection at all times in order to play the game, along with having your GPS signal turned on.