Q:

How to make part of the model not be subdivided？ 

I would like to create a standard square groove in the plane, just like this. 
But when i switch to object mode, it just almost disappear because I used subdivision. 

A:

Same example:

Becomes:

The solution is:
1.  Select the edges you don't want to be subdivided

In the right bar (Press N to show it) set the "Mean Crease" value to 1 (it sets how much the selected edges don't react to subdivision smoothness Edit: note that the face is still subdivided but the subfaces created by subdivision mantain the original position.  No smoothness.).  They'll become violet. 

Turn back to Edit Mode and enjoy

