Daru is the resource used to upgrade units and their abilities (including enlightenment level) in the Barracks. With the addition of the Treasure Hunt, it is also required to complete treasure hunt attempts.
One Daru is granted for every one of your units that dies. This only applies to units that stay dead (and have to be replaced) - units that die against the World Boss, or on defense against city looters, do not grant you Daru.
A few thousand Daru can be obtained anywhere that a random item can be obtained. Such as after each victory while adventuring or as the reward for completing a duel or quest.
While adventuring, you may come across an ancient burial ground (the name changes to fit the theme of the region). Looting it yields a level-appropriate quantity of Daru (usually in the thousands) or may get you in a fight with the burial ground's sentinels. These are about equal to the other fights in the adventure in difficulty. These range from a fight with a single enemy in a single battle to an entire group of enemies of waves of two or more.
In the Wilds, you will sometimes find bands of monsters wandering around. Killing them will yield a few Daru Pearls. Each can be converted to 1000 Daru per pearl by clicking them in your inventory. In addition, troops that die give you Daru (see above under Unit Deaths). Killing Wandering Managogs yields no other benefit.
You could also buy troops and disband them for Daru, but you only get one Daru for every five troops. This is mostly recommended only if you need a few hundreds or thousands and don't have time for battle. You can get more by the troops dying, e.g. by fighting Wandering Managogs (see above).
You can fish the yellow small fish for 10,000 daru. If your fishing tank is a higher level more daru will be caught.