It means their username somehow reflect the contents of the comment
For example, if your username is u/geefunken, and you make a comment about a funk musical artist whose name starts with "G", someone might say, "Username checks out" – because you posted something similar to your username
July 24, 2020 at 08:43AM
via reddit https://www.reddit.com/r/explainlikeimfive/comments/hx12g7/eli5_user_name_checks_out/fz32oba?utm_source=ifttt