Twitter has "verified" celebrity, business, and other official Twitter accounts for some time, but Facebook's verification process is fairly new. Surprisingly, few government bodies have gone through the process for verifying their Facebook pages, maybe because verification has not been widely publicized. Verification can be beneficial to government bodies concerned about impersonation or parody accounts that can often confuse and mislead the public.
You will know if a government page is a verified page if it has a blue checkmark next to its name. For example, the City of Evanston's Facebook page is verified - check out the blue checkmark next to the City's name on its Facebook home page here.
The process for verifying your government Facebook page is as easy as filling out a form that looks like this (see below). After receipt of the form, Facebook will review the information provided, and if approved, place the checkmark on your page.