Nycgal.........well, you already know from the other responses that what is "deeded" to you, you own, and is not considered to be part of the "common " grounds shared by all.
With a deeded backyard, as mentioned, you actually own it, and may make use of it.....that's the good news!!
However..............just know that there still may be restrictions on how it is used..........for example,...rules regarding the use of barbeque grills or placing any kind of structure on it (ie - a hot tub). Anything you might want to do with the land will be specifically listed in the bylaws of the association. ( Bylaws, among other things, are a list of community rules for - they also list whose responsibility it is to maintain certain items).
Check to see if the association is responsible for maintaining the "deeded" yard - as you might be responsible for the lawn care, or even a deck or patio if it exists.
I have seen townhome complexes where the association took care of the front lawn maintenance, but not the rear yard...in my complex, they take care of decks, but not patios! It can vary.
Every assocation handles things differently, so be sure to take a look at the community bylaws in advance of buying, or at least ask these questions ahead of time, so you have a clear picture of what is specified.
Prudential NJ Properties