Pokemon GO features a variety of Items that will either be given to you from the start, found in the wide world by visiting places like PokeStops, or bought in the in-game Shop. Below is a list of known items and what they are used for.
Pokeballs are a trainer's main tool, and are used to try and capture Pokemon. You'll be given 50 to start with, and you can either find more by interacting with PokeStops, or purchasing them from the Shop in batches of 20, 100, or 200 in exchange for PokeCoins.
Incense can be used to lure Pokemon out of hiding and increase the rate at which you can find Pokemon hiding in the wild for at least 30 minutes of use. To begin you'll be given two Incense, and more can be bought from the Store in a batch of either 1, 8, or 25 in exchange for PokeCoins.
This item is automatically given to you at the start of your adventure, and allows you to easily photograph your encounter with a Pokemon in the wild. Just tap the camera icon during an encounter!
The Egg Incubator is used in Egg Hatching for the Pokemon Eggs you can find in the wild in such places like visiting PokeStops. When an Egg is placed in an Egg Incubator, the player must travel a certain distance tracked by the phone's GPS before the egg will hatch. Only one incubator is given at the start of the game and can be used as many times as needed, but more fragile versions to incubate mulitple eggs can be bought in the Store that will break after 3 uses.
Lucky Eggs, unlike regular Pokemon Eggs, are used as consumables that increase your overall experience gain by double the amount for a period of 30 minutes. You can purchase them on the Shop in batches of 1, 8, or 25 in exchange for PokeCoins.
A Lure Module is a more sophiscated version of incense that attracts Pokemon to a particular PokeStop for a period of 30 minutes. Not only is it more effective, but it also targets the Pokestop not just for the player, but all players interacting with the PokeStop during that period! It can be bought from the Shop in groups of either 1 or 8 in exchange for PokeCoins.
Your Bag is where you store all of your non-Pokemon Items, which include Pokeballs and the like. To start with, your bag can fit up to 350 different items (including your camera and incubator). To get more space for your bag, you need to buy a Bag Upgrade from the Shop to fit 50 more items per upgrade.
Your Pokemon Storage is where you keep all of the Pokemon and Pokemon Eggs you find in your travels. When you begin the game, your Pokemon Storage can hold up to 250 different Pokemon, and 9 Pokemon Eggs. In order to hold more in storage, you need to buy a Pokemon Storage Upgrade from the Shop to fit 50 more Pokemon per upgrade.