Basically the ballhead is the attachment point from a tripod or monopod to the camera with, yes, a ball joint to allow you rotate, tilt and hold the camera in that position. typically with a quick release plate. Or another way to say that is, you don't screw the camera directly to a tripod.
What should I be looking for in my next ballhead or maybe a better question is what do YOU have and why do you like/dislike it? What say ye?
integrated bubble levels?
handles or knobs for adjustments?
grip-handle (seems kinda cool)?
light weight? big and burly?
I have the lower end Bogen/manfrotto and it's OK, It serves it's purpose.