In Destiny, Motes of Light are a form of currency that you can use to trade with The Speaker which you can find in the Tower or on Earth, or with Xûr, Agent of the Nine when he is in the Tower.
You will only find Xûr in the Tower on the weekends, so you’ll have to save your Motes of Light during the week and visit him in the weekend to purchase the loot you want.
You can acquire Motes of Light in multiple ways.
You will automatically receive a Mote of Light once you reach level 20, and after that any XP you acquire will go toward gaining another Mote of Light.
Motes of Light can also be awarded randomly in the following ways: