From the Super Mario Wiki
Special Points are a stat in Mario & Luigi: Bowser's Inside Story. They are functionally identical to Bros. Points from other Mario & Luigi games and are needed for Mario, Luigi, and Bowser to perform Special Attacks. As Mario, Luigi, and Bowser gain levels and obtain better pieces of clothing, their maximum amounts of SP increases. Certain pieces of clothing will also reduce the SP cost of Special Attacks when worn. SP can be refilled by using Syrup Jars or the effects of the Bro Badge.