From postgres documentation,
client_min_messages (enum)
Controls which message levels are sent to the client. Valid values are DEBUG5, DEBUG4, DEBUG3, DEBUG2, DEBUG1, LOG, NOTICE, WARNING, ERROR, FATAL, and PANIC. Each level includes all the levels that follow it. The later the level, the fewer messages are sent. The default is NOTICE. Note that LOG has a different rank here than in log_min_messages.
I am assuming that these messages are not the same as the results (PQResult) of the commands executed. If so, how do I read these messages through libpq? Would there be an impact of these messages on the application`s performance?
Messages are sent as a different message type on the PostgreSQL protocol, usually interleaved with the result stream. libpq sees them and picks them out, then adds them to a queue of notifications you can examine.
See the manual.