The purpose of a Korban Chatas brought by an individual is to remove his accidental sin. There are some private Chataos where there is an argument regarding exactly why there are brought (such as the Chatas of a Nazir and a Yoledes).

There are many different types of Korban Chatas brought by the public. Each has a different purpose, although each revolves around some type of sin. Here, too, there are some sacrifices where the sin is somewhat obscure, such as the public Chatas brought on Rosh Chodesh regarding which the Gemara says in Chulin (60b) that Hash-m is asking us to bring a Chatas for him because he lessened the moon (there are many explanations regarding what this exactly means). Each public Chatas must be analyzed on a case to case basis. There are many Gemaros that discuss the different public Chataos, and why each one is brought.

All the best,

Yaakov Montrose