A thicket generally is closely planted shrubs and such to provide cover, nesting, etc.
In an area where I have shrubs, the limbs go almost to the ground and birds run around on the ground underneath there, rabbits too.
A lot depends on what you have room for. Here's an article on thickets that's interesting.

Here is a link that might be useful: Thicket Establishment

Hey Christie,great information. I have a spot in the back corner that is the beginning of a thicket! Unfortunately, that's right where the neighbors toilet their dog. I guess I'll have to put up a fence in that area. Pet out!