A cage is your bird's sanctuary. Birds require a lot from a cage for physical and psychological well being.
Even small birds need space to flit, while large birds need space to flap wings or play with toys. Without the right cage, a bird may have behavior problems, including the nastiest, those most hard to deal with - aggression, feather plucking, screaming, and phobias.
A too-small cage does not allow room for toys and other accessories that are vital for making the cage an enriching environment. A too-large cage can be intimidating for shy birds. A flight cage or aviary, which will not be your bird's main domicile, can be as big as you wish as long as bar spacing is narrow enough so your bird does not get his head caught between, wide enough to accommodate perching, yet not so wide that your bird can escape. Proper bar spacing is important for cages as well.