Earning rewards through Battles and Quests will sometimes provide you with duplicates of Units you already own. You can use these duplicates to upgrade Units.
Navigate to your Warband screen and you will see a bar with a number below each Unit.
When this bar and the number count is full, the bar will turn green and an upgrade arrow will display.
Click into this Unit and select the upgrade button to increase the level of this Unit. You will receive a prompt displaying the improvements that will be made before you confirm. Upgrading Units costs coins as well as other Units.