I see GMs and players complain about the "I hit it with my axe" limited view of combat. People often feel that if the rules don't facilitate a more narrative approach than it's not "part of the game".
I personally don't feel this is the games responsibility, the rules are the structure and dice are the hand of rate. Story should be facilitated by the storytellers, Both the GM/DM and players. I feel many GMs miss golden opportunities to help player to help themselves. Narrative combat makes the game more exciting, and narrative driven combat makes the GM's job easier.
The two biggest opportunities for this is during the players action, both before and after the die is rolled. These might seem like a no brainer to some, but stay with me.
Two very simple phrases GMs can use to help players get into combat as narration is "what do you do? Describe it", and "what does/did it look like?"
"What do you do? Describe it".
Before the player rolls the dice, ask the player to describe their attack. Ask for quick details about weapon swings or how the character is moving. To further facilitate narrative combat do the same with monsters and NPCs. Describe the grimace on the orcs face, the assassin's fast blade slashes, and the sneer on the city guards face as he sets his spear.
"what does/did it look like?"
Take the narrative and apply it after the roll as well. After the player rolls ask the player to describe the effects of the dice roll. Use the player's description to guide the reactions of other combatants. After the player describes jumping from the cart, while sinking his dagger into the guard smirking, describe how the other guards react. Give the characters description impact, nothing would be less rewarding and more discouraging to a player than to give an amazing description, just to be met with a none narrative reaction.