Sacrificing in the Old Testament was not about appeasing God, but was meant to be about love. Saying “I love you so much, I’m going to give you this grain or animal that is really important to my livelihood.” It was the act of giving.
Christ’s death on the cross therefore, was the ultimate sacrifice. It was the ultimate act of love. He gave himself so that we could live.
Therefore, the entire Eucharist plays out like a sacrifice on an alter of old. But it is Christ offering himself on the cross for our salvation, as it happens. It transcends time. We have to imagine it is actually happening now.
The priest is a proxy for Christ, the alter is the cross, and He is sacrificing Himself to us for everything. He’s saying “I love you so much, I give you my life.” Christ is the priest, sacrificing not grain, not a lamb, but himself.
The priest says, “Your own of Your own, we offer to You, in all and for all”. What does that all mean? Well, in other words, simply, Christ is saying, “I give myself to you.”