Stats
In the Kingdom, there are 6 stats that you need to worry about. Of these, there are 3 main stats:

Muscle
Muscle is as you would expect, a measure of your physical strength. It is used in combat to determine your chances of hitting. It is also used to determine your level if you are either a Seal Clubber or Turtle Tamer.

Mysticality
Mysticality displays how attuned you are magically and mystically. It is used mainly to calculate your maximum MP (explained below) and it determines how effective certain skills are. It is also used to determine your level if you are either a Pastamancer or Saucerors.

Moxie
Moxie is a measure of your style, cheek and your slyness. It is used in combat to determine the chance that you are hit by enemy attack. It is also used to determine your level if you are either an Accordion Thief or Disco Bandit.

Whilst adventuring, you will gain experience in each of these three stat areas. You may notice that you have just gained "3 Chutzpah" for example. This would mean that you are building up your Moxie. When enough of these points have been accumulated, you will  increase your primary stat. Then, when the primary stat is high enough, you will advance a level.

After you have built your primary stat, you will notice that you need more points to advance to build the next stat point. The same occurs when you advance a level.

There are 3 further stats that are equally important to your character:

HP
HP obviously stands for Hit Points, but its much easier to shorten it. In reality, the more HP you have, the more damage your character can take. There are of course ways to rebuild your HP, such as waiting till the rollover, resting at your campsite and taking special items.

MP
MP has three different names for the different classes. For Seal Clubbers and Turtle Tamers, it stands for Muscularity Points. For Pastamancers and Saucerors, it stands for Mana Points. Finally, for Accordion Thieves and Disco Bandits, it stands for Mojo Points.

MP is used when your character uses its skills. There are ways to rebuild your MP, such as waiting till rollover, resting at your campsite and taking special items.

Inebriety
Inebriety shortened, means drunkenness. If you drink too much, you cannot adventure anymore until the following day. Unlike HP and MP, you cannot regain your soberness. I think that there used to be sober pills in the game but they all disappeared a while ago.