A fine mess ....
Firstly let's look at a very human situation.
You've been neglecting your wife. Perhaps it's the middle of the World Cup, or the rugby home internationals or maybe, unforgiveably, you have no valid excuse. Television and/or sport has taken her place in your affections and you have failed to notice it. But she does and, very soon, makes sure that you do too! You're in the doghouse and, worst of all, there's no TV there!
At this stage you are miles apart from her and only you can bridge that gap. So you send her flowers and say nice things. You have made your offering, not quite a sacrifice, but have you seen the cost of carnations these days? The gap is bridged ... for now. You are forgiven ... for now. You are reconciled ... for now. You have received the marital equivalent of atonement.
Of course, this is a crude example, you can hardly compare your relationship with your wife to your relationship with God, but there are similarities.
Atonement means 'God and Man being reconciled'. It's not a permanent thing, the people of the Old Testament needed to seek atonement, through the giving of sacrifice, as a sort of on-going thing. The first thing that Noah did when he came out of the ark was to build an altar and sacrifice some of the animals (hopefully not making them extinct in the process). The Bible tells us that God found this acceptable.
It wasn't that God liked the sight of blood, or of death, or even enjoyed the aroma of the burnt offering as it wafted up into his spiritual nostrils! It was the physical act, the intention of the man giving the sacrifice that was important.
As long there was true contriteness and awe in the heart, then the atonement was true and the sacrifice provided an, albeit temporary, reconciliation with God.