A revJohn reader recently asked me about a source for the Jewish understanding of sacrifice. Like Christians, I'm sure the answer would vary, depending of the Jewish community sourced. But here is one site, Judaism 101, that provides a helpful look at the concept of animal sacrifices. The article points out that Jews do not now offer animal sacrifices because the authorized place of sacrifice, the Temple in Jerusalem, was destroyed by the Romans in 70 C.E. The author of this entry believes, however, that when the messiah comes, sacrifices will resume. Until then, forgiveness for Jews is obtained through repentance, prayer, and good deeds. See the article here.
It is helpful for me to see that after 2,000 years the concept of animal sacrifice is still seen, in some Jewish communities, as something that God desires. So it is not surprising to me that first century Jews who actually approached God in this manner and who became followers of Jesus of Nazareth and who struggled to find meaning to his cruel and horrific death, would conceptualize this event as "blood sacrifice" and as an "atonement for sin."