When users sign up to Twitter, people should have a verified email and phone number, also have a profile photo that reflects individuals or the company name.
The verified accounts will filter their mentions filtering those from other verified accounts, and it cannot be private, that username must remain the same. However, it seems it is the only real feature, or a perk comes with a blue badge aside from bragging rights.
If you get rejected, the reapplication process will after 30 days, and it will require a direct connection to a Twitter representative.
Twitter has originally released these update to verify the authenticity of users.