MP is energy which is used to pay costs in Baten Kaitos Origins's card battling system.
Activating cards without cost such as armor, weapons, weak attack, medium attack, and strong attack raise MP slightly for each card activated. There are also cards which are used to raise MP quickly such as Warrior's Scarf and Force.
Special attacks, and some artifact/item cards which heal and revive characters cost MP.
When the MP level reaches 5, the maximum, the player can activate MP Burst which allows cards to be activated without cost for the entire round making Relay Combos (consecutive attacks from 2 or 3 members from your party) much easier. After MP Burst is finished, the player's MP level is reduced to 0.