Can someone explain the concept of Jesus "dying for our sins"?

I usually brush over this whole thing because I really don’t get it. But maybe someone can make this whole thing make more sense to me. Was this a “human” sacrifice? And if so, what did that accomplish? Did god sacrifice himself to himself to satisfy his own blood lust, or was doing this necessary to accomplish something? And whatever was accomplished, could it have been done a different way?

I’m particularly interested in the Christian take here. I was brought up a Catholic, and we just never went into this in detail, although we were always told that “Jesus died for your sins. That’s how much he loves us.” I can’t wrap my head around this.