As you may've figured it out, it's the same verb used twice. It's the equivalent of the english "make somebody do something", so the meaning is kind of "to force someone to do something"; obviously, you can replace the second verb "fare" with any other verb. I'll try writing some sentences with this expressions, with the equivalent translation of the english version so as to understand the meaning:
1- Gli ho fatto fare i compiti ; I made him do his homework
2- Le ho fatto guardare il film che ho scelto ; I made her watch the movie I picked
3- Mi hanno fatto andare da un dottore per una visita ; They made me go to the doctor for a check up
I hope this helps. If you still have some doubts, feel free to ask.