Which keyboard is it?

The majority of keyboards used by consumers are rubber dome over membrane keyboards. You can read about it here.

Many people will refer to these as "rubber dome" or "membrane" keyboards, despite that being less accurate due to exceptions (ie, Topre switches use rubber domes, but not membranes, and the Model M could use a membrane with mechanical switches).

If you are using a low profile or laptop keyboard, it is likely using scissor switches which are essentially the same as above with the addition of a scissor mechanism for stability.

Why are mechanical keyboards so much better than this other type?

It depends. In general, the use of other keyboard switch technology is merely a cost or space saving measure. No matter how high quality they are, they are generally designed around being cheap and easy to make.

Most mechanical switches are designed to be switches, and then they are used in keyboards. Rather than a sheet of contacts as in a membrane with rubber domes, you have individual switches, usually mounted in a metal plate (called a backplate), and then connected to a PCB under that. All of this is in a case and keycaps are put on the switches.

The ability to get different switches and to change keycaps is seen as a great benefit as well.