This is where you will find Poké Balls, Potions, Razz Berries and a host of other items. When you arrive at a Pokéstop you can swipe across the screen and the Pokéstop sign will spin and various items will fall out allowing you to tap them to pick them up. You can also simply tap the X button to close the Pokéstop and claim all the items without tapping them individually.
Pokéstops are also a great place to find lots of Pokémon. To make wild Pokémon appear you can use the Lure Module. Once plugged into a Pokéstop, Pokémon will start to appear. The great thing about Lure Modules is that the Pokémon that appear for you will also appear for other Pokémon players gathered at the same Pokéstop.
As Lure Modules are hard to come by I tend to look on the map for Pokéstops that already have a Lure Module inserted and head towards it and catch lots of Pokémon for free. That assumes there are other players nearby also out hunting Pokémon but with the popularity of the game you will usually find some Pokéstops with Lure Moduled inserted.
If you live in a town or city there will be many Pokéstops, often very close together. If you live in a rural location they are harder to come by and will need you to do a bit of exploration to find them. The picture below demonstrates the town/rural divide when it comes to Pokémon hunting:
On the left is my local town of Weymouth and on the right is a road in the middle of the Dorset countryside. Not much going on in the countryside! Stick to the towns and cities.