The detail of Adam and Eve’s “sin covering” is not given in their Biblical account. It only states that God made or “killed” an animal to cover them with the skin.
Throughout the Old Testament we see the picture of the altar and the sacrifice. So through this we conclude that Adam and Eve understood the importance of the sacrificial animal to cover their sins. This understanding that they had was passed on to their children and then carried on from generation to generation.
In today's culture of animal rights, we would look at the sacrifice of an animal as cruel and barbaric. But, at the same time we kill 4,000 babies a day in the name of "choice." We take these types of stands today because we do not fully appreciate the seriousness of sin as God sees sin.
In the Old Testament, the sacrifice of animals stands as a reminder of our own guilt before God and the need for our Lord Jesus Christ to stand as a substitute for us. Adam and Eve understood that innocent animals died in their place so that they could have a relationship with the Father and hopefully re-enter that time of worship they had once enjoyed.
Place yourself in Old Testament times for a minute. The people were mostly tillers of the land, (farmers). They raised those innocent lambs from birth. The people would have grieved over the death of their little lamb knowing that it should be them that died for their sins and not their animals. Sin is costly. Coming back to a place of worship is costly.
The bottom line of the teaching of Adam and Eve is that if we are to return to a place of worship, a place of walking hand-in-hand with God daily then we must deal with our sin God’s way, which is embracing the work of a cruel rugged cross and the death of an innocent savior on our behalf.