The engineering is used to create fun items, trinkets, pets, mounts, head gear, and more! There are plenty of neat tricks that an engineer can learn and an endless amount of gadgets are at their disposal. Most things are made out of metal, so mining is the gathering skill most commonly associated with it.
Jewelcrafting was the new profession introduced in TBC expansion. For jewelcrafters, they not only can craft rings, necklaces and trinkets, as well as a few fun limited use items but they can cut gems, imbuing them with special powers depending on their color and cut. These gems found while mining are used to enhance gear items that contain sockets when the jewelcrafter prospects ore, so the most logical gathering pairing is the Mining tradeskill.
The tailoring is different in that the materials needed for it are not found with a gathering tradeskill. Varying types of cloth drops of mobs in the open world, no matter who picks them up. Tailors can use this cloth to craft cloth armor, cloaks, bags, and magical spellthreads that are embroidered onto armor to give it bonuses. Because tailoring produces a lot of magical items and doesn't require a gathering skill, it is often combined with Enchanting.
Enchanting, much like tailoring, isn't associated with a gathering skill. Rather, the materials needed for enchanting are gathered by using the Disenchant skill associated with the trade. Magical items: Uncommon, Rare, or Epic quality items with bonuses can be disenchanted into materials, destroying the item. Those materials can be used to add bonuses to other armor or weapons. Because Enchanting uses a lot of magical items and doesn't require a gathering skill, it is often combined with Tailoring.

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