The blue or yellow check mark icons are identity verification badges.
The blue identity verification badge means that a member's identity has been verified with a government ID.
The yellow identity verification badge means that a member's identity has been verified with a government ID, but their profile name is different from the legal name that was verified. Here's an example of how that could happen: if a member uses a business name for their profile, that name will not match the first and last name used on the government ID they submitted for their identity verification.