An account that has been Twitter verified is one that has been authenticated as to the actual identity of the person using the account. This helps ward off fake profiles and those that may mimic you or your company in an attempt to fool other users, defame or otherwise bring harm to you. The blue Verified badge on Twitter lets people know that an account of public interest is authentic.
https://help.twitter.com/en/managing-your-account/about-twitter-verified-accounts