What is sin and how we are to understand it and its role in human life?
Well, the sin is basically when you do something against logic and common sense. It can be criminal in nature (like murder) or non-criminal (at least according to human laws) like female promiscuity.
Regardless, the most important thing here that every single little action that each one of us make has an equal reaction from the universe. Things that we do that are not rational usually get a negative reaction from the universe and this is what we basically call sin.
According to the Torah, the only way to atone for sin is usually with blood. Usually animal (for less serious sins) but sometimes - human blood (for more serious). There is no way around this and rational people should be able to agree with this statement.
Why blood? Well, according to the Torah, soul is in the blood, which means that to repair the damage to the world from sin, someone has to give up their soul and therefore blood. Thank God, Yahuah is a just and merciful God, so he usually requires just the blood of the animal, which is a good substitute for human blood obviously.
Torah is just and it preaches justice for all (not just for some or for most). Therefore, it is an eye for an eye, tooth for a tooth, injury for injury, blood for blood, soul for soul. I think in this sense Torah is a very wise Law and book in general.