Fight scenes can do all the same things for a story that sex scenes do; they are actually far more alike than they are different. Through a fight scene, a writer can develop characters, change character relationships, resolve or introduce conflict, defuse or ratchet up tension, and push plot points all while providing action that alters the story’s pacing.
You can really get to know a character by watching her fight, by seeing what she chooses to do, or not do, in a tense or dangerous situation. The character who elects to fight bare-handed is different from the one who draws a weapon at the first sign of trouble. Does the character delight in the fight or grimly acknowledge it as an ugly necessity? Perhaps the character is a pacifist who refuses to fight. How does she react when she’s outmatched and is it different from her reaction when she’s the superior combatant? Does she kill? Does she show mercy? Seeing the protagonist on the page, and understanding her motivation behind use of trash talk or intimidation lets the reader understand her a lot more in a short time. A fight scene gives you the opportunity to address any of these situations, and dozens of others, in character.
It’s pretty obvious that fight scenes can provide conflict resolution, but they can also be a source for introducing conflict. A bar fight could start our heroine on the path toward the end point of the story (however far away it may be). It could be the event that ignites a quest or mission, or maybe she has to skip town to avoid assault charges. Ta-da, conflict. Fights have almost become a trope ending for a novel or series, with the protagonist facing off with the antagonist for one last showdown. The reason it’s done so often, is that it works well, which is also why we don’t complain about the lack of originality in structure. This technique also works for wrapping up smaller arcs that occur within a more layered plot.
Tension is closely related to conflict, so it’s easy to see how fight scenes can influence this. A fight can be cathartic for the protagonist or the story, letting off some tension before a scene or chapter that won’t function properly with too much impending doom hanging over it. Likewise, strategically placed fight scenes can increase the sense of danger. If the characters are well written, the reader will be invested and concerned on their behalf. This can be a huge bonus in longer works and for writers with weaker plot skills, because character and tension together can greatly improve reader interest while masking less developed plot.
Plot can be pushed forward by a fight scene in much the same way character can be revealed. This can be done in fragments, perhaps with the protagonist gaining insight through banter or bargaining during or after the confrontation. It can also be done in large chunks, with the outcome of the fight directly shoving the protagonist in the right direction.
Any time a scene can do more than one thing for the story, it’s a win for the writer. It allows you to include more layered complexity without going over your word budget or boring your readers. Fight scenes are also a lot of fun to read, which means plotting and writing them can be fun too… if you like that sort of thing.