Or "subject separation" is, essentially, the difference between how sharp and defined your subject is vs. how sharp and defined the background behind the subject is.
It is usually implied that the subject is well separated, meaning that the background is out of focus. 
Factors that affect separation are:
* distance subject - background: the more the distance, the greater the separation all else equal
* f-stop (if you can control that): the bigger the aperture ("faster" or smaller f-stop number), the greater the separation all else equal
* focal length (if you can control that): the longer (e.g. use an 85mm lens instead of a 35mm one), the greater the separation all else equal
* the size of the camera's sensor: the bigger (e.g. full frame DSLR vs. mobile phone camera), the greater the separation all else equal

Assuming you can control all or some of those variables, how much separation do you want to achieve? This is an aesthetic question, it depends on your taste, your style, on the type of background and on the purpose of the image. Generally speaking, I like editorial photography in location and I like to show the background, therefore I am not a big fan of blurring the background into oblivion. The important thing is to have control so that you have the options available.

The shot below was taken on the rooftop of a warehouse in Brooklyn. I used a fast 200mm lens (Canon f/2L IS) that gave me a fantastic control on the separation. In this case I wanted the background to be visible enough so that viewers understand the location but not enough to distract from the attitude Maria was giving me :) Lighted with a ProFoto B1 Air 500 with a pass-through white umbrella.

http://www.robertodemicheli.com/people/Models/Nicklaus1/slides/_MG_5228-1%20-%20V4.jpg