What does this bag with a checkmark on it next to Roblox usernames mean?

The icon means the user was verified by the roblox system.

Some popular users have had trouble with imposters using their display name (since it does not have to be unique), or a lookalike username to scam others. The checkmark allows others to see that the account is more likely genuine as there are some requirements attached before you can get one.

I have not yet found what these requirements are, or how the process of getting this icon next to a username works. It might be associated with an in-app purchase (as it's likely such users can be trusted, for they have something to lose if their account is banned).