The VPN is sort of like the old expatriate standby, the mail forwarding service, which would work for Netflix physical DVDs.
You give Netflix an address in the US. As far as they know, that's where you get your mail. They mail a DVD there. Someone at that location puts it in another envelope and mails it overseas to you. When you're done, you mail it back to your forwarding service. They take it out of the international envelope and put the Netflix envelope in the US mail. Netflix has no way of knowing you're overseas.
Exactly the same thing happens with a VPN. The data from Netflix goes to a network address located in the US. That site forwards the data to your overseas address, and forwards data you send back.