What does the error message "psql: error: connection to server on socket "/tmp/.s.PGSQL.5432" failed: No such file or directory" mean?

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The error message suggests that the Postgres server is not running or has crashed. The client is unable to establish a connection with the server because the socket file it's trying to connect to does not exist. This can also happen if the socket file's location has been changed, or if there is an issue with the Postgres configuration.