Wearing the item and repairing it yourself are two different things:

To actually wear the item, you have to be on the same level with the item and your class must be on the item's job list. (i.e. Headgear Item Level 10 for Disciple of War Classes can be worn once you are level 10 and your class is one of the 5 Disciples of War. Said item can't be worn by the other three groups of Disciple Classes)

To repair the item, two options are available to be done. First you let the NPC do this for you at the cost of some gil. Second, you do the repairs yourself with the class requirement and at the cost of some materials. The first one is self-explanatory so I'll only provide an example for the second one. (i.e Leather Headgear requires LeatherWorker Lv. 3 to be "self" repaired. This item can only be "self" repaired when you are using the LeatherWorker class that is at level 3 and above. The materials to repair may vary)

Hope this helps.