To be precise, Twitter wasn’t being hacked but instead its DNS is compromised. To put that in simple plain English, when a users enter at the browser, the DNS that store the actual address of twitter is suppose to direct traffic to (the actual address for twitter). What happens was the compromised DNS direct traffic to another website.

If on that day itself a user were to enter twitter at his browser, the browser will be direct to another site but if the user enter he still get to go to twitter.

This is the news excerpt reports from AP

Fri, Dec 18 2009

Hackers briefly blocked access to the popular Internet messaging service Twitter, steering traffic to another Web site where a group reportedly calling itself the "Iranian Cyber Army" claimed responsibility.

Users trying to reach Twitter early Friday were redirected to a Web page that CNN reported had a picture of a green flag and a message that said, "This site has been hacked by the Iranian Cyber Army."

There was no evidence the hackers are actually linked to Iran. Web sites like Twitter and Facebook helped bring attention to the Iranian opposition during the country's crackdown after its June elections, with users posting minute-by-minute updates and amateur video.

Twitter later Friday posted a message on its blog that said its Domain Name Systems' records "were temporarily compromised but have now been fixed." The site says it will update with more details "once we've investigated more fully."