The WOW skills are grouped into several categories: professions, secondary skills, weapon skills, class skills, armor proficiencies, and languages. Your character's skills can be viewed on the skills tab of your character sheet. Professions are the major trade skills, which are available to all classes, such as tailoring and mining.

A WOW character can only have two professions at any given time. Secondary skills, such as fishing and first aid, there are also trade skills, but it have no restriction on how many can be learned. Weapon skills include all weapons that a character is able to use the WOW gold skills. Many weapon skills need to be learned, as your character only starts with a handful of skills, it can learn to this skills. Some WOW class skills are determined by your character class (granted at character creation) and are an integral part of your character. Armor skills are known from character creation, or received from trainers or talents.
 
How do you improve your skills and professions?

Basically, players improve their skills through usage. While the WOW class skills automatically increase, you have a character levels, weapon skills and trade skills only improve through usage. Thus, in order to improve your ability with swords, you must equip and fight with a sword. Professions and secondary skills operate similarly. In order to increase your skill level in a profession or secondary skill, you must use it.

What are skill caps and how do they raise?

The WOW skill caps are the maximum level that you can currently raise a given skill. Skill caps are raised by leveling (weapon skills) and by receiving training (professions and secondary skills). For the weapon skills, gaining a level of experience will raise the cap for each weapon skill by 5 WOW Leveling. For trade skills, your profession rank - apprentice, journeyman, expert, artisan, and master - determines your maximum skill level. These ranks are gained by receiving training (from NPCs and/or books) and have minimum skill and level requirements.