When you're trying to understand something, and you finally understand it, you've "figured it out". 

Aya figured out how to hook up the webcam, so now we can video chat with you guys!

You can also "figure out" a problem, which means that you find a solution to the problem:

I'm two months late on my rent, and I still can't find a job. I need to figure something out or I'm going to be out on the street.

The object of "figure out" can come in two different places: 

• figure (something) out
• figure out (something)

Pronouns like "it", "them", etc. go between "figure" and "out". Most other words can go in both locations.