"Verification badges
are applied to a YouTube channel's connected Google+ identity. This badges help to visually confirm the authenticity of a brand. When you find the badge on a channel for a popular celebrity or business, you can be sure that the channel actually belongs to them. The verification tick only appears to the right of the channel name, and "Verified" appears in a pop-up if you point your cursor at it.
These badges are applied with discretion to applicable official businesses, brands, organisations and public figures."
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They are basically to verify that they are the official channel, so famous people such as PewDiePie have one and fake ones don't