The Forge is a building located in the main base island which allows you to upgrade your troops.
If you have the required resources (and the camp level of the troop is the same level or higher than the upgrade level you want) you may initiate a troop upgrade.
Each troop upgrade roughly increases each of the troops' stats by 10%, and takes a certain amount time to upgrade, of which increases with each level. Some of the earlier upgrades may only take a few minutes, whereas the latest ones take more than one day.
Arguably, a troop level upgrade is more significant than a hero stat boost, as one upgrade can increase the statistics of numerous troops. For example, whereas an upgrade to Freya will only increase her individual stats by 10%, and upgrade to Serfs may increase the stats of three equipped squads of 8 Serfs, which overall has a dramatically greater impact.