Why would they force you to use their DNS servers.
You would need to ask them to know for sure. Of the top of my head, here are a few possible reasons.
To reduce problems (and maybe support calls) caused by incorrectly configured DNS Servers.
They may also have internal websites and systems whose addresses aren't published and hence would not be known to external dns servers.
Some viruses change the dns server on their victims computers. (This means you could type mail.google.com or try to login to your bank and end up at a specially crafted website designed to capture your logon details). By forcing you to use their servers, they protect you from that type of attack (assuming their servers are clear). (Note, this doesn't stop viruses from messing around with your hosts file to achieve the same result).
How it is achieved technically?
They can configure their firewall to block outgoing DNS, ie port 53, from anything other their dns servers.