Some Pages and profiles have been verified by Facebook to let people know that they’re authentic. If you see a blue badge on a Page or profile, it means that Facebook confirmed that this is the authentic Page or profile for this public figure, media company or brand. If you see a gray badge on a Page, it means that Facebook confirmed that this is an authentic Page for this business or organization.
As a normal Facebook user we all create account or page with our name and it is also possible to create multiple account on same name. Their are number of same name pages or account for any celebrity, public figure or for any business.So Facebook take serious step to make clear that which one is official and all the rest of others are not. This verification show that the page or profile your are visiting official represent someone or maybe a request by official owners.
Some tips to verify your page
Your Page must contain an official website.
Your official website must be in good condition.
Your website should contain Facebook LikeBox.
Your page must have a good amount of Fans.
You must have to run Facebook Ads.
Your FanPage info must be writing fully with active address.
You also have FanPages on other social networks like GooglePlus, Twitter etc.
Your Page should be active.