Each multiplayer battle you fight, you lose a battle credit. At 0 battle credits you will no longer be able to fight a mulitplayer fight. You gain one every 20 minutes up untill you've got 15 credits, then you will stop gaining them. There are other ways to gain them (achievements, clans) which allow you to go past 15 battle credits. You will not lose any for going over the max of 15 however you will stop gaining credits untill you drop below 15 again.

Battle Credits can also be bought once you've ran out.

Hope that covers everything