Basically put, subframes are just chunks of a full frame. In the case of our novas, there is a subframe on the front. When you pop the hood and take a look in the engine bay, you will notice that it looks just like a full framed car with 2 frame rails. However, if you look under the car, you will see that the frame rails are bolted directly to the floor pan of the vehicle. This was so GM could make cheaper econo cars and lighter, but was found out to be pretty good performance handling too, and thus the X-body economy (Nova)and then the F-body performance (Camaro, Firebird) cars were born (they share front subframes in the same years).
They are pretty good setups, and you can remove the subframe from the front of the car, however, this is not really recommended unless you know what you are doing, and then only if the bushings need replaced. It's pretty easy to not get it on plumb, then you will have a "sidewinder" car.
If you are going to put any kind of performance engine into that car, subframe connectors are a must. They connect the front and rear subframes together to make the car stiff like a full framed car. Otherwise you may wind up with a twisted floor pan the first time you step on the gas!