Stat
KoL has three main stats used to express the strengths and weaknesses of your character: Muscle, Mysticality and Moxie. Each stat has two classes which rely upon it to advance levels. The Seal Clubber and Turtle Tamer rely upon Muscle. The Pastamancer and Sauceror rely upon Mysticality. The Disco Bandit and Accordion Thief rely upon Moxie. This is the primary stat for each class. When a player of level n reaches n2 + 4 points in their primary stat, they gain a level. For instance, a level 14 player reaches 142+4=200 points in their primary stat, the player advances to level 15.
See the page on Advancement for information on how stats increase.
Minimum Mainstat
Many locations require you to have a minimum number in your character's main stat in order to adventure there (NB this is your current modified stat, not your base stat):