Storm Points (SP) are points you gather by pretty much doing anything in Ninja Storm 2. After you gather a set number of SP, you'll unlock something new, like a title or a character (Press X in main menu to see how many points are required for the next reward)
You win them by completing fights (any game mode) or completing requests (Ultimate Adventure).
Fights: You can win SP by finishing a fight, doesn't matter if you win or lose, but of couse you'll win many, many more points with a victory. You'll receive a rank showing how well you did, and you are aiming for a S. With a S you win 1.5x bonus SP. Other ranks will net you less bonus points. (The lowest I got so far has been a D with 1.1x bonus points)
Any fight counts. Free Battles against the computer, a 2nd player, every fight in the Ultimate Adventure or playing online.
Tip: If you really want an easy SP boost, use a 2nd controller and play 1P vs 2P in Free Battle. I did it once to see if it worked and I won around 9000 points with one battle since it was pretty much a perfect match.
Ultimate Adventure: throughout the story, you'll receive optional missions you can complete. Besides winning cash and items, you also receive SP.