A user group is a set of users grouped by a name. A user may be a part of several user groups.
For example, the Marketing Dpt user group gathers all the users in the Marketing Department of the company. The Managers user group gathers all the users who are manager of a department. Some users can be in the Marketing Dpt only.
What is the aim?
Well, we gathered people in groups of users. It's great but what is the aim?
In fact, it will be very useful for you, if you want to give different permissions to the users, according to the user groups they are in. This is an Enterprise Edition feature.
If you want to know more about how to set up these advanced permissions, take a look at the Build you user groups article.
In the Community Edition, there is no permission applied on user groups. If you want to benefit from this feature, you'll have to upgrade to the Enterprise Edition.