What do you do? The basic gameplay loop of Pokémon Go is to catch random pokémon. You can play it entirely as a collector, just trying to get as many species as possible. For this approach rare variants called "shinies" that have a slightly different appearance from the base specimens are highly sought after. You can also play it as more of simple RPG, looking for the pokémon with the best statistics and attacks for either group PvE (taking down raid bosses), PvP battles with other players, or attacking and defending gyms. You have to pick which of three global teams, Instinct, Mystic or Valor, that you will associate yourself with when you start playing.
What is the world like? In addition to random pokémon wandering all around you, the game adds Stops and Gyms to the world. A Stop is an area with a disk that you can spin every five minutes for random items (e.g., balls that you use to catch pokémon, potions to heal your pokemon). Gyms are buildings that can also be used to get supplies of items like a stop, but primarily are the focus of asynchronous PvP battles. They are also the areas where raid bosses, which often require teams of players to take down, can be challenged.
|This is what the game looks like if you play in a more public area. You can see a stop and three gyms in the background, as well as a new pokémon species that was recently released.|
Asynchronous interactions: Gym battles. If a gym is held by a players of a different team, you can fight the pokémon in the gym to take it over. It can take a while to defeat everyone in a gym that has a really good defensive team, but it is quite doable even with fairly weak pokémon. The exception to this is if owners of the pokémon defending the gym are actively healing them as you fight. A determined defender with a lot of resources can hold you off, but this is extremely rare.
|Far and away the main thing you do is catch and manage pokémon. Here I am trying to catch a Trubbish, the trashbag pokémon, one of the newer designs.|
Is it good exercise? It depends. If you are in an urban area with lots of stops and gyms, walking around to spin them for goodies and to look for new pokémon is really helpful. However, if you are out in the country, in many areas there are no stops and no gyms. In these locations, it doesn't make much difference whether you walk around or not. Pokémon will generally only spawn if you are burning incense, and that works almost as well sitting on your couch as it does walking around. When I lived on the city I got a lot of exercise walking from the game. Now that I live in a rural area, I get very little exercise from it unless I decide to go into town.