Although Fatigue is not a skill in itself, it affects all your other skills. As you gain experience in your skills, you will get fatigued.
You can see your level of fatigue in the stats menu. When you reach 100 percent fatigue you will no longer gain experience in your skills. Some skills such as mining, fishing and woodcutting you will not be able to continue to do at all.
To reduce your fatigue you will need to go to sleep. To sleep either find a bed and click to rest on it, or if you have a sleeping bag in your inventory click to rest on that. Beds can be found in many buildings and are marked on our world map. You are given a sleeping bag during the RuneScape tutorial and can also buy them from general stores.
When you go to sleep you will see your fatigue at the top of the screen- this will quickly reduce as you sleep. At the bottom of the screen you will see a word which you will need to type in when you want to wake up.
If you are attacked while you are asleep you will immediately wake up but will not have any of your fatigue restored.