The Rank is one of the two strength indicators of a regiment. It goes from 1 to 23 and is increased by obtaining XP. The max rank is capped by your current Warlord Level. That means, your regiments can never have a higher rank than the value of your own Warlord Level.
How to get XP
Each regiment collects their own XP. XP is obtained by participating in victorious battles. For each defeated enemy regiment, your regiments will get an equal part of XP. The more battles you win, the more XP your regiments get!
Another source of XP is sending your regiments to expeditions in Sky Arch or applying Knowledge Potions.
Benefits of reaching a new Rank
Each new Rank will allow regiments to get more Upgrades to increase their attributes and perform better in battles.