Google+ launched its process to get profiles verified, so people should be aware that the Celebrity, Brand or Public Figures are real, not fake profile or pages. The verified profile has a Verified Profile Badge Google Plus badge after their names. The profiles have been verified by Google itself.
Remember: This feature is only available to Public Figures, Celebrities, Brands and people have been added to large amount of Circles.
If you are looking to apply to get your Google+ profile verified, here is the link got get your profile verified.
Q. I have been added in large amount of Circles, how can i get my profile verified?
A. If you have been added in large amount of Circles, and if Google consider you, than they will contact you manually, there is no method to apply for that.
Q. I have seen verified profile of people added in small amount of Circles?
A. They have used Knol available in Google+ to verify profile, but it is not removed.
Q. My profile name is verified, and i want to change my name, will that verification badge removed?
A. Yes, If you have a verified name in Google+, and want to change your name, if you do so, your verification badge will be removed and you have to get your profile verified again. If you have got verified your profile through Knol, than you will not be able to verify it again because it has been removed from the product.
Q. How many people should add me in their Circles so that Google+ considers me to get profile verified?
A. You must be added in large amount of Circles, so that Google+ may notice you to get your profile verified, they didn’t told what is large for them, but the standards will be raising with their product is growing.
Original Source : Google Plus Blog Info