DNS is a kind of Internet directory service that just resolves hostnames (like netflix.com) into IP addresses.
So what they do with this is, that you configure your device to ask their DNS server to resolve names of select services that they intermediate. This way netflix's IP address is replaced in their DNS records with the IP address of their own proxy. Your AppleTV is fooled to send connection request to their proxy instead of directly to netflix.com. They will relay it further to netflix, of course, just coming from their host (which has US-based IP address). This will camouflage your request as coming from US.
Doing all this via simple change of DNS setup in your house makes this process very simple to you (you just need to change this one number), but requires more effort from the service provider's part.
If the company providing this service can be trusted, then you should have nothing to worry about.