Block someone and you are never put in a room together again - their sessions stop showing on your schedule, and yours stop showing on theirs. It is completely silent: they are never told, and it looks no different from never having crossed paths.
Because it works both ways, blocking means fewer sessions to choose from, for both of you. That is worth knowing before you use it - and it is reversible: you can unblock anyone in Settings → Safety tools.
Blocking happens as part of filing a report: tick Also block when you send one, whether that is during a session (the ⋯ menu on a tile), from a host's profile, or from the recap afterwards.