Professions, formerly known as Trade Skills are non-combat jobs that your character can take on which lets them craft weapons and items, or improve them. Your character may have up to 2 professions, and any number of secondary skills (lesser professions). Complete and updates profession guides can be found at Skryer.
Professions have different level requirements which require you to be higher in level to advance, so that you can't just craft all day along to become good. There are 3 types of professions:
Gathering Professions - These are the raw material skills that are needed in order to craft items, some may find these useful just to trading, and some may use these to gather resources for their own crafting.
Herbalism
Mining
Skinning
Production Professions - These jobs enable you to create and enhance items which are cheaper and more powerful than the ones sold at vendors. A lot of good items can be bought and sold from crafters.
Alchemy
