Revive items are used in a way that you would expect a revive item to work. During gym battles your Pokemon may end up fainting. If this happens you can use the revive item to bring the Pokemon back to life so he can continue fighting. When you use the revive it will bring the Pokemon back with full HP.
You can purchase revives from the in game store using coins, or you can collect them from Pokemon stops after you have reached level 5.