MP stands for "Mana Points" or "Magic Points" in some cases. Magic Points are used for casting Spells and using Skills. Some characters specialize in the use of Magic and will have greater MP available to use than other characters (For more information on character MP statistics see characters pages.). When a character has their MP reduced to zero then no more magic can be cast. Some skills, like Prayer do not require MP.
MP is used for a variety of things, from healing and resurrecting your fallen allies to wiping the smile from your enemy's face. This means that it is important to keep all of your characters in good MP. MP can be restored by the use of items like Mana Herb or Mana Capsule which can be purchased from item shops. It is also possible to have the HP and MP of your entire party restored for free by simply entering the World Map and returning to the screen you were in.
There are also Blue Orbs scattered throughout the world which are sometimes found next to save points. Walk into one of these blue orbs and your health and magic points will be restored. Also, if you save and reload the save, your MP (and HP) will be at full.