A trainer is an NPC who allows you to advance to a higher class tier. Upon talking to them, they allow you to accept your advancement as well as clone beforehand if you have a clone credit (which you likely will since you obtain one automatically when reaching an the advancement levels 5, 15 and 30).

Trainers are located in most major bases and can be seen as a blue shield icon () on the map window, though their icons are filtered off by default, as well as the mini map.