The level to repair a piece of gear is 10 levels below the level to equip that piece of gear (well, except for items that are level 10 or below, in which case you just need level 1 of the corresponding craft). So if you can equip something at level 15, then you can repair it when you have the correct crafting class at level 5. If you can equip something at level 50, then you can repair it when you have the correct crafting class at level 40. When your crafting classes are level 50, you can repair any gear in the game (at least until another expansion raises the level cap above 60).
Each piece of gear identifies in its tooltip which class can repair it. If it's a craftable item, it will be the same class that makes it. (Or, if non-craftable, the class that makes similar types of gear.)
(It used to be that we had to actually switch to the appropriate crafting class to do the repairs, but they've changed that rule so that now we only need to have the appropriate crafting class unlocked and leveled to the required level. So long as we meet the requirements, we can do the repairs while on any class/job.)