Twitter and now Facebook verify some accounts. Famous people are often impersonated online with sometimes humorous but more likely offensive accounts. To make sure fans are getting posts, pictures, opinions and information from the source (or at least the staff of the source) accounts can be verified in an arrangement with the famous person and Facebook or Twitter.
A verified account on both Twitter and Facebook has a blue circle with a white tick inside.
Both Facebook and Twitter do not accept requests to verify accounts, rather you are invited to have your account verified. A quick Internet search shows a couple of rumours about what is required to have your account verified. There are reports that simply being famous is not enough, others suggest that the amount spent on advertising can lead to a verified account. Whatever the process is, it is good (but sometimes embarrassing) to know that an account that has been verified is the official Facebook or Twitter of your favourite actor, politician, business or sports star.