War is the continuation of politics by other means.
—Carl von Clausewitz
My stage combat mentor, Gregory Hoffman , likes to say that a fight is what happens when words are insufficient to express the intentions of the characters. Just as in a musical the characters sometimes burst into song as a form of heightened speech, so in a play with fights the characters burst into physical violence. The fight is a continuation of the dialog by other means. And just as your dialog should be “intentional,” so should your fights.
Characters are defined by their actions, and speech is action. This is something all playwrights know but novelists sometimes forget. When a character speaks, they are trying to accomplish something, however indirectly, and whether they’re fully conscious of it or not.  Your characters may not be aware of their specific intentions, but you, as the writer, must be.
When I direct a play, I ask my actors to label the intention of every line. These labels usually take the form of -ing words—shaming, rebuking, admiring, begging, disarming, feinting—the more specific, the better.
Consider, for example, these two lines from the beginning of the fight between Young Siward and Macbeth:
Young Siward: What is thy name?
Macbeth: Thou’lt be afraid to hear it.
The obvious, but generic and boring, labels for these two lines would be asking and telling, respectively. We can do better. Young Siward is inexperienced, alone and probably afraid. What’s he trying to accomplish? Is he blustering, trying to present a false front of courage? Is he challenging an unknown fighter? Or does he recognize Macbeth and is dreading a response? And Macbeth, is he daring Young Siward? Mocking him? Or is he bolstering his own spirits? The specificity of these labels creates variety and interest, which is critical for performing Shakespeare, lest it devolve into mere poetry. 
When I’m directing a fight, I don’t necessarily ask my combatants to use labels (or “actions,” as they’re typically called), but I do ask them to consider the intention of every move of their choreography. Is the thrust to to the low line intended as a killing blow? Or is it meant to draw the parry, opening up the high line? Is the belly cut meant to land? Or just drive the opponent back to gain breathing room? Again, the specificity of these choices are what elevate a fight scene from a boisterous clanging of swords to a dangerous confrontation between motivated characters.
If you’re a playwright, you have a whole team of people—actors, designers, directors—bringing the intentions of your characters to life. If you’re writing prose, that burden falls entirely on you and your reader. On the other hand, you have a distinct advantage in that you don’t have to choreograph every move—you can resort to narrative summary.  If you’re following my scheme of populating a high-level structure with storytelling moments at the inflection points, then you can reserve the blow-by-blow for those moments, as long as the intention is clear throughout.
Bonus dialog tip: Readers should be able to distinguish characters from each other by their speech. If you cover up the attributions—e.g. Inigo said, or The Man in Black said—you should still be able to tell who’s speaking from the way they speak. This is certainly true of The Princess Bride, where you’d have no trouble distinguishing the unidentified dialog of Inigo, Fezzik, Vizzini, Westley, Buttercup, Miracle Max, etc.
The same principle applies to fights, and the characterizations in The Princess Bride extend into the fights. Inigo is an expert swordsman who fights with chivalry. Fezzik is friendly and straightforward and relies on his size and strength. Vizzini favors his wits and deception, and is undone by his arrogance.
Romeo and Juliet also has great examples of this. Mercutio prefers a swashbuckling, cut-and-thrust style, while actively mocking Tybalt’s precision pointwork, calling him “the very butcher of a silk button” who “fights by the book of arithmetic.” Paris adheres to the rule of law, while Romeo fights like a caged animal.
Next time: the nitty-gritty. Actual fight moves. Actual words. I’ll offer up a fight scene I wrote as an exercise and analyze what works and what doesn’t.
1. Gregory Hoffman is the founder of Dueling Arts International.
2. If your dialog is flabby or unrealistic, one reason may be that the characters are serving your intentions, e.g. conveying exposition, rather than their own.
3. The power of playing an intention is so great that it can literally render words redundant. A few years ago I directed a production of A Midsummer Night’s Dream where they actors spoke entirely in an invented language. No one in the audience understood the words they were speaking, but they were all clear on the characters’ intentions and had no trouble following, and enjoying, the story.
4. In principle you could use narrative summary in a stage fight—anything is possible in theatre—but I’ve never seen it done.