You can think of "MP" as some type of Mental Potential.
So, Mages and the likes channel that energy into casting overt spells.
However, Monks could certainly use that to, say, strengthen their attacks or defense (buffs/debuffs), or even for a Ultra-Powerful Mega Strike.
Interestingly, in real life, one monk threw a punch in which he literally moved his hand ONE INCH (his body didn't move much either). He did this in New York City, in a testing facility. His punch went into a crash test dummy which was being monitored. The result showed he put as much force behind that punch as a 3,000 pound car moving 20 MPH. This video is on Youtube somewhere. And it shows the absolutely amazing potential we have, even in real life for stuff like this.
So it's easy to see in a high magic world (i.e. classic fantasy), how Warriors could channel their MP into devastating attacks or ultra-powerful one-use Defense moves.
Also, maybe characters can Share their MP, so a Magic User might even give some of his MP to the Warrior who will use it to Ultraslash the entire enemy group.
The game Dragon Quest IX does exactly this. Pretty much ALL of the most useful and powerful attacks and buffs/debuffs take MP to use. Yet only a few classes use that potential for actual spells.
In novels, the Codex Alera series has everyone (except the main character who doesn't seem to have any MP) using their MP for a variety of mundane and combat specific abilities. And only a handful of abilities would resemble actual "spells," so 95% of what people do with them, even in the midst of battle, we would classify as buffs/debuffs. But they are used to devastating effect.
So, really, MP can be used anytime you want to have Powerful Abilities which are limited in their use but which can be used at the start of battle. Even in a modern, science-based setting, MP makes a GREAT stand-in for ammo --- say every Gunshot takes 1 MP (which would be renamed something like "Ammo", or "AM" for short).