Hi Mike,
Receiving is quite interesting concept in Ariba. Below are few key points covered by receiving module in buyer.
1) Acceptance - Mark order as received in Ariba (full receiving or partial receiving)
2) Rejection - Received goods are rejected probably because they are not in good condition or contaminated.
3) Over Tolerance - This is really good concept for receiving in which client might be interested if you have change orders enabled. User doesn't really have to change an order to increase the quantities if it under the tolerance limit.
4) Close an order - If user is just intended to close a partially received order, then they can close it while receiving with partially accepted quantities.
Amit