Aggression can mean a lot of different things. Most owners are describing behaviours that they feel are threatening when referring to aggression. Commonly this can be biting where there's an injury, biting where there's no injuring, growling, barking, lunging, air snapping, etc.
Sometimes the reason for "aggressive" behaviour is clear and other times it's not. For many dogs they start with low level behaviour such as growling and progress to more serious threats when they realize that it works. Other dogs may suddenly develop "aggression".
The first step would be to rule out medical issues. An animal in pain will not act like they usually do and might respond to touch in a dramatic fashion. When my dog Tank had a knee injury he began to shown aggressive behaviour when dogs came near that part of his body. He would snarl, growl and even air snap. This was unusual for him and a clear sign that something was wrong.
Another cause for aggression is often fear. This can not be understated. Dogs who are scared will run or fight. We humans unwittingly trap our dogs with leashes, walls, kennels, etc and can trigger a bite when a dog really just wants to avoid.
Dogs can be fearful of anything! Common issues include fear of strangers, kids, loss of a valuable resource (ball, sock, food) and of course other dogs. If we treat aggression (fear) with physical violence or force then we are often pushing the dog to escalate his/her own aggression. A better approach would be to use slow desensitization to the source of the fear so our dogs learn to deal with it.
Aggression is one of those behaviours that needs to be treated with care. It's imperative that you seek help from a professional trainer or behaviourist and veterinarian. For more information please contact Where's Your Sit or the Association of Pet Dog Trainers (APDT).