Tanner is the skill associated with the tanning labor. Tanners turn raw skins from butchered animals into usable leather at a tanner's shop. They have to act fast, as raw skins will rot fairly soon after being created. By default, this job will automatically be queued when skin is produced, but this can be deactivated from the orders-workshops menu.
If you're still not getting the hide tanned, enter the order "tan a hide" manually in the manager menu (j-m) with a sufficient amount.
High proficiency in the tanning skill only affects how quickly the raw skin is processed, as leather does not have quality modifiers. However, when a large number of skins needs to be processed, perhaps after butchering a large quantity of livestock, time is of the essence. This can also be solved by having multiple tanneries and tanners available.