It's not uncommon to experience physical conflict within a dream, and while it's true that it's not quite the same as getting into a fight in real life, it is quite telling when it comes to what's going on in your waking life.
Naturally, fighting in a dream represents some kind of conflict and/or confrontation in your life. You could be at odds with someone, perhaps somebody who has a bad attitude towards you or else is preventing you from moving forward from a situation. Perhaps you are struggling with some strong and difficult emotions, such as jealousy, bitterness or judgement, with regards to someone else, or even just a particular situation that you have found yourself in and are attempting to resist it.
Fighting doesn't always have to represent something bad, however. If you find yourself trading blows in your sleep it could be a sign that you are trying to overcome some kind of trauma, or you are tackling some serious problems head on. Maybe you are no longer prepared to put up with an issue or a person anymore, and you're standing up for yourself and what you believe in.
Alternatively, you could be trying hard to prove yourself. Perhaps you've done something wrong in the past and you are determined to show that you're not that person anymore, or even that people are not taking you seriously and you're about to show them who you really are.
If you are watching a fight between two other people, it could represent that you're somehow being forced in the middle of conflicts between people you are close to. It could also represent two opposing sides of yourself - beliefs, values or goals - that you can't reconcile, or that you are being forced to choose between two different paths.
If you are fighting for your life with feelings of desperation and fear, it might be a sign that you're overwhelmed in certain areas of your life, or even that you are facing a serious health condition.