In order to receive an item, you must go to the Item Event Log (you can get there from your Inventory) and Accept or Reject the item. If you don't accept or reject within 2 days, it will automatically be returned to the sender.
Neopets FAQ wrote:
Why didn't I receive an item my friend sent me? Why didn't my friend receive an item I sent them?
Whenever an item is given between two users, the recipient must accept or reject the item at their Item Event Log.
If the item is accepted, it will appear in their inventory, if it is rejected, it will be sent back to the sender.
If the item has not been accepted or rejected within 48 hours of it being sent, it will be returned to the sender.
Please be cautious of who you accept items from. If you do not know the sender and the item is a fairly valuable one, it may be best to simply reject it.