Either their service is down - which rarely happens - and in that case you should just try later, or you have internet connections on your computer. If you're able to connect to other websites, then your computer is not the problem.
Another possibility is that you're trying to connect to Facebook via a computer/network that blocked Facebook (such as a work place, a school, etc.).
Some dates when Facebook was actually down:
On September 23, 2010, Facebook was showing DNS failure when you tried to reach their site. This seemed to be the case for most visitors.
Other general comments from our users about Facebook:
Chat with our AI personalities
Server is down, server is overloaded with people and cannot respond, your being blocked (Either your own internet settings or facebook is refusing to connect to you), your internet sucks
You can access Facebook at: http://www.facebook.com You can find the DNS details using a WHOIS search.
It's a glitch or the server is busy.
If you can't post anything on Facebook, try deleting cookies and restarting your browser. If that doesn't work it may be a problem with the Facebook server.
No.