This is a slightly tricky question to answer as it cuts across various aspects of feral cat behaviour.
The first point to make is that not all feral cats fight as the question implies. You’ll see fairly harmonious feral cat colonies with hierarchies of sorts which keeps the relationships in balance.
However, feral cats are whole cats; they have neither been neutered nor spayed. Neutered male cats (castrated) are less likely to become involved in cat fights and vice versa. They tend to have female characters.
Whole (unfixed) feral tom cats, driven by testosterone might be aggressive towards other males in three instances where a fight might break out.
Dominance over another male is one possibility. If the relationship between two males is neither dominant nor submissive a fight might occur for one to establish dominance over another.
Fighting over the rights to mate with a receptive female (in estrus) may, but it seems will rarely, occur.
“Contrary to what one might expect, fights are rare, but an older dominant male probably gets most of the matings.” (Wild Cats of the World quoting from The domestic cat: The biology if its behaviour).
And finally, male cats will develop a home range which will overlap with other male cats. They will avoid each other through scent marking. If they come into contact with each other a fight might ensue to protect their home range. This is probably the most likely reason for feral cats to fight.
It seems that feral cats are less resistant to fighting than dogs. They are prepared to engage in a fight rather than deal with it through posturing. Cat fights can be horrendously aggressive.
Female Feral Cats Cooperate
It would seem that the position regarding female feral cats is quite different within feral cat colonies. At the heart of larger feral cat colonies there are several queens (female breeding cats) who are often related and who help each other in a variety of ways to assist with the survival of their offspring. They assist each other during parturition. They may nurse, groom and guard each other’s kittens. This is called reciprocal altruism and most likely occurs when small favours are exchanged.
I have been very brief. If someone would like to add to the page you are very welcome.