From the Super Mario Wiki
Special Points are used in the Mario & Luigi franchise. They are needed for Mario, Luigi, and Bowser to perform Special Attacks. They make their only appearance in Mario & Luigi: Bowser's Inside Story, but similar to Bros. Points from Mario & Luigi: Superstar Saga, Mario & Luigi: Dream Team, and Mario & Luigi: Paper Jam. The only difference is both bros can use any special attack unlike in Mario & Luigi: Superstar Saga where a bro was restricted to their own bros attacks. Some attacks can be reduced to lower costs to keep the points longer without using Syrup Jars to gain more SP.
As the SP meter goes down, attacks that use large amounts of SP become unavailable, and Syrup Jars must be used to refill the SP. As Mario, Luigi, and Bowser gain levels and better pieces of Clothing, their maximum amounts of SP available increases.