Units, buildings and spells can all be upgraded twice, but you need to merge 2 level 2 units to make a level 3 one. This is not always the best choice until mid-to-late game, as it can be overkill against weak ennemies and thins your other lanes, but it is essential in the late game: you'll obtain powerful units able to go toe-to-toe with knights easier, and making a level 3 unit gives you a high-tier unit to buy in the roster. Plus, level 3 spells are a blast!
You don't have to "do" anything to upgrade the tier, you just gain access to more powerful units as the game goes on.