In MMO games, Crafting is an ability to create a new item of resources in your inventory. It's usually divided into various specialization, such as blacksmithing or cooking. Even though, in some MMOs, you can choose a character class that will receive benefits when creating specific items.
In most cases, the Craft feature used to make an additional challenge for players. It's a simple system: if you want to develop the best character in the game, you have to create the most durable armour and weapon; to do this, you need to spend a lot of your time in the game, grinding various resources. This model looks much more explicit than usual 'grind for an item' system because of the random part of it hidden in the resource gathering part. This clarity attracts players: it is much more honest to see how much resources you have left to gather before crafting a new item than blindly wait for it to drop from the enemy.
Some games use craft as a supplementary system of character improvement, but in other MMO games with Crafting, this feature used as an essential activity. It is especially common for the sandbox games: you start with a weak character that has no instruments or resources, and your main goal is to survive using all the items you can find. Usually, in such games, using the craft function, you can also create various furnishings, or construct buildings.
In some MMOs with Crafting, these concepts combine. Many RPG games have housing feature, so you can craft various items for your home and decorate it, or even create buildings and different useful constructions on your territory. It gives a huge space for creativity.
Moreover, usually, you can create not only weapons, armour or furniture. It can also be various potions, valuable ingredients, or items used for quests and professions.