This feature is being provided by twitter to prevent identity confusion, and to know which accounts are 'real' and authentic. That means twitter has been in contact with the person or entity the account is representing and verified that it is approved. This also does not mean that accounts without the 'Verified Account' badge are fake. Twitter has only verified a handful of accounts to help with cases of mistaken identity or impersonation.
One other way to identify an account that twitter has not verified is to check the official web site of the person and see if there's a link back to their Twitter profile.
Twitter has started with verifying well-known artists, athletes, actors, public officials, and public agencies. It may verify more accounts in the future, but because of the cost and time required, twitter is testing this feature with a small set of folks for the time being.
If you feel that if your account is constantly competing with parody or impersonation accounts then you can fill this feedback_form ( http://twitter.com/account/verify_request ) to get your account verified. But the first thing you should do is to provide a link to your official website on the twitter profile page and also link this back on your website.
For businesses you can fill this feedback form for business accounts, though twitter at present is not testing this feature with businesses.
Please remember that this feature is still in beta and Twitter verifies a limited number of accounts, submitting a request does not guarantee account verification.
For more information check this : http://twitter.com/help/verified
To see lists of Verified accounts , check the various lists at http://twitter.com/verified