Taken directly from the game, these skills are how you get things done. Many have obvious uses, but some can be used for things you would not immediately think of. Skills are also based on Attributes of your Character and can gain bonuses or penalties based on these.
You check skills by rolling a D20 and adding your total skill modifier. For example: You are trying to climb a rock wall. You have 12 DEX (+1 Modifier) and have 5 ranks in Agility. Your total skill modifier is +6 for agility. You roll 9 on your D20 plus your 6 modifier, getting 15. You succeed and climb the wall.
Agility (DEX): How swift you are on your feet, in the air, and the water. This is what is used when you need to climb or make any other difficult move action.
Constitution (CON): How healthy you are and how well you take care of yourself. For each +1 you gain 5 Health. A starting character gets 10 Health. This is also used to concentrate on aiming, charging spells, and praying.
Construction (DEX): How good you are building structures or evaluating the stability of existing structures.
Cooking (WIS): You ability to cook, identify, or modify foods.
Crafting (INT): How good you are at making things with precious materials.
Divination (WIS): Your ability to sync with the Anima Mundi and harness its power.
Dungeoneering (WIS): How adept you are at delving into dark reaches and coming back alive. This is your ability to survive and track indoors.
Farming (WIS): Your ability to nurture nature as well as identify general flora and fauna.
Firemaking (WIS): How well you can light fires, distinguish what started fires, or extinguish fires.
Fishing (DEX): Your ability to catch things in the water.
Fletching (DEX): Your skill at making projectiles. Modifies Ranged damage.
Herblore (INT): Your ability to identify herbs and make potions, as well as identify potions that are already made.
Hunter (WIS): How well you can track animals and people. Also your ability to survive in the wilderness.
Invention (INT)(Needs +5 in 2 of Crafting/Smithing/Divination): How easy you can develop new technology. Requires a good knowledge of other Artisan skills.
Magic (WIS): Your ability to use spells. Damage is modified by Runecrafting.
Mining (STR): How well you can prospect and extract ore from rocks.
Prayer (CHA): How pious you are and how likely the gods are to hear you.
Runecrafting (INT): Your ability to imbue magic and craft runes. Modifies Magic damage.
Slayer (WIS): Your ability to identify unfamiliar opponents and their potential weaknesses.
Smithing (STR): How well you can work metal and inspect metal items.
Summoning (CHA): How in-tune you are with spirits, as well as your ability to call upon them.
Thieving (DEX): Your ability to steal from people as well as your ability to remain undetected.
Woodcutting (STR): How good you are at felling trees and recovering usable wood.