This question could require a lot more, but I will give the bare minimum for basic understanding.
When Adam and Eve committed the original sin (Genesis 3) the consequence was death. The first time we see this consequence is when God kills the animal to clothe them in animal skin. Thus, blood was shed as a result of their sin. Death remains the consequence of Sin, and like all people we will one day die, because our entire world has been contaminated with Sin. God however, allowed men and women to live on this earth in spite of their sin, and he began to set in place ways for people to “atone” for their sin. Animal sacrifice was a practice of atoning for their sin. Instead of receiving the penalty of death, God would transfer the penalty to an animal, thus the penalty of death was still carried out for Sin. This is a root part of the meaning of atonement (at-one-ment), because it allowed the people to be one with God even though the deserved death and eternal separation.
Unfortunately this was only a temporary fix for the situation because sin was so great. The reason that we do not continue this practice today is because Jesus received the penalty once and for all. No longer would a sheep, a cow, or a goat need to be sacrificed, and no longer do we need to live under the consequence of our sin, because Jesus took the penalty that we deserved and satisfied the wrath that God had for our disobedience. This is called substitutionary atonement. There are many different good analogies that describe Christ’s atonement for our sins, but this is the most common and it is one of the fundamental beliefs of Christian faith.
Remember that God is both perfectly just and perfectly loving. Sometimes it seems like the two cannot coexist, because if justice is to be done perfectly then everyone God loves deserves death, but if God is to love perfectly how can he bring death to those he loves. It is a huge conundrum and that is why Jesus was the only way to redeem, or fix, the situation. God could bring his perfect justice on Jesus. Paul says that on the cross “he became sin for us” even though he was perfect in every way. This substitution of Christ in our place satisfied God’s nature as one who is perfectly just, and allowed him to continue loving us by opening the door for eternal life.