You can increase your Warlord Level by gaining Warlord XP. Warlord XP is obtained when applying Upgrades to your regiments from the Upgrade Tab on the main menu.
Each upgrade will grant a different amount of Warlord XP, based on the cost and the rarity of the upgrade itself.
The maximum rank of your regiments cannot exceed the value of your Warlord Level. For instance, if you are Warlord Level 8, you will not be able to rank up a regiment to level 9 before improving your Warlord Level first.
Also, provinces on the map usually have Warlord Level restrictions, too. Reach the required Warlord Level first, before you can scout those areas.
When reaching a new Warlord Level, you will also receive a nice Diamond reward!