3D Programming, Matrix4 Explanation

I know the basics of the Matrix4 struct in (in this situation I am referring to the one in OpenTK), like it is used to hold data related to the camera translation, rotation, eye vector, etc. But can someone provide me with a better explanation about the class, like how and why it is used in most—if not all—3D games for representing this data.

The sourcecode(which is not very well documented in my opinion)to the Matrix4 struct is located here