Brewing is a profession that specializes in potion and poison making using ingredients primarily gathered from Botany.
Brewing requires the use of a brewing cauldron, which serves as a crafting station. You may find cauldrons in every major town and sometimes in other buildings and locations.
To begin brewing you do not need to train the skill other than you need to aquire the recipe to craft each potion or poison.
Some recipes are taught by purchasing and reading the recipe from a merchant. Others are found as drops from monsters or within chests.
Potions are beneficial items that can be used in battle, unlike food or drink which can only be used out of battle. Currently potions are only usable on yourself. But there are plans for Splash potions which will heal you and your allies.
Poisons are offensive items that you can use in battle to damage or affect an enemy. There take up your potion slot in battle so it requires extra caution.