Brewing is the skill which requires mixing ingredients together in a Vial of Water to create potions. The potions' effects are various, from gaining materials like stardust or oil to reducing combat cooldown, so those potions are basically used to support other skills.
There are three types of potions:
Level 1-30 potions which need a (small) Vial Of Water
Players train Brewing by creating potions. High level potions give more XP. The XP increase scales poorly however, making it one of the costliest skills to level. Another factor which contributes to that is the fact that brewing doesn't have a tool that is upgradable with gems to enhance, unlike Mining, Crafting or Fishing.
Brewing level gives a bonus duration to all potions, which scales up to 20% longer at 100 level (or 2% every 10 levels).
Completing the Mixology quest will allow players to unlock the Mixing Stand, which can be used to mix new potions from other potions. Brewing Scrolls are required as formulae/recipes to mix. Those can be found from various locations. Even whilst mixing potions give XP, it still doesn't stop brewing from being the most difficult skill to level.
After completing the Witches Potion quest, players can craft a Brewing Kit. The kit gives a 10% chance for any potion made to produce an additional Potion at no extra cost or experience gained, or 20% with a Green Brewing Kit Orb.