The armorsmith skill is used to make all metal armor and shields at a metalsmith's forge (or magma forge). The corresponding labor is armoring. The construction of leather armor is done by a leatherworker.
Like all artisans in Dwarf Fortress, skilled armorsmiths make armor more quickly, and of a higher quality, than unskilled dwarves. The higher the quality of armor, the more damage it can block, which helps to minimize casualties in combat. A legendary+5 armorsmith is potentially the most valuable dwarf any fortress could hope to have. This makes armorsmith skill a very popular choice in starting builds.
 Training armorsmiths
To train an armorsmith to legendary (or legendary+5, better still), you must have him or her make hundreds of pieces of armor. Use iron for this (or copper, if you have a lot of it): save your precious steel or bronze for after the training is done (though you may opt to make a few steel suits early on for your soldiers to wear).
These hundreds of pieces of armor will rapidly clutter the forge, greatly slowing down the smithy's progress. To keep up with a high-skill armorsmith, you must employ several full-time haulers to clear out the shop: either item haulers, to drag the pieces to nearby armor stockpiles, or refuse haulers, to drag the items to a nearby dump. (Dumping, however, requires periodically redesignating the area over the forge ( - - ) in order to mark its contents for dumping.) Setting up several forges and having the smith move from one to the next when they get cluttered works well in concert with multiple haulers. You can also employ a spare metalsmith of any sort to keep destroying and rebuilding the forges to clear them out.
Alternatively, you can have some of your farmers, fishers, and hunters (or anybody else who has no moodable skills) forge a single piece of armor and hope that one of them enters a strange mood, as producing a piece of artifact armor will instantly push them to Legendary+1 (unless they were unlucky and got Possessed).