Star Points are in Paper Mario and Paper Mario: The Thousand Year Door. They are green orbs with yellow stars inside them that let the player level up. They are gained from every enemy except optional bosses and enemies deemed to weak to the player's level in Paper Mario. Collecting 100 of them allows the player to level up, in which the player can choose to raise their HP amount, BP amount, or FP amount. The harder the enemy, the more Star Points are obtained.
In Paper Mario you can no longer gain any Star Points after you're level 27, though the Star Points Level of the monster can exceed it. And in its sequel any enemies except Amazy Dayzee will stop giving you Star Points after level 37.