Your inventory is where gifts and sale packages are stored. It can be found on the rightmost tab of the inbox by tapping the envelope icon on the bottom left corner of the HUD.

Why cant I claim something from my inventory? 
The number of certain inventory items that you can collect at a time is limited. If you see an error saying you cannot claim additional items, you must use the ones you have first. For troops, this means dropping them in battle, whereas blessings must be used up before dropping more on your map.