Dominant dog behavior is behavior that dogs engage in to protect access to the stuff they want - food, favorite beds, and attention from their people are some examples of they stuff that dogs value. They want to be able to get these things first before others do. This 'domainance-aggression' is the behavior the 'dominant' dog will display to others that are ranked below him.
Not all bad or rude behavior means that a dog is dominant. Sometimes they're just spoiled and used to getting their own way. In other dogs, however, they are willing to assert themselves over other dogs in order to get the stuff they want. For example, a dominant dog might decide to mount another dog. If the other dog is submissive, they may just allow it or try to move away, in which case the dominant dog might snap or snarl to show to put the other dog in its place. If the other dog is also dominant, however, it may snap or snarl and a fight could start since neither dog is willing to back down.
Other behaviors like growling, snapping, or freezing when someone gets near coveted food or toys, or doing stuff the dog doesn't like (grooming, picking them up, etc)... or refusing to acknowledge commands that the dog clearly understands... are ways to assert dominance over people. For example, the dog might decide to lay on the coveted couch. When his owner tries to remove him, he may freeze and show his teeth, making the person back off.
On the other hand, some behaviors aren't necessarily dominance. Let's say the dog is on the couch. His person sees him, shouts at him to get off and approaches the dog aggressively. The dog may also show his teeth - but not necessarily in a display of dominance, but in a display of fear because he's reacting to how his person is behaving. It may not occur to him to simply get off the couch since he is afraid.
If your dog displays dominant-aggressive behaviors, you can avoid situations or triggers that cause these behaviors... and use cheerful "happy-talk" to help defuse the situation. However, learning how to work with your dog to re-train and manage him is a better option. Look for a qualified dog trainer or behaviorist with experience in dominant dog behavior. The trainer should focus on positive methods rather than harsh corrective methods. Properly dealing with dominance issues can lead to both happier dogs and happier pet owners.