What style of icing is this please?
If you are talking about the sculptural elements, the icing used to create those is called fondant. 

The name fondant comes from the french for melting.  It has a consistency somewhere between play dough and tootsie rolls.

Here is a good tutorial on making fondant.  It can also be purchased.  You can find millions of tutorials on how to work with fondant.  The tutorials tend to focus and what is being sculpted.  If you are looking for a very simple how-to for working with fondant this is a good tutorial