syslogd is the Linux system logging utility that take care of filling up your files in /var/log when it is asked to. On a standard system, logging is only done on the local drive. But syslog can be configured to receive logging from a remote client, or to send logging to a remote syslog server.
Some of the use cases could be:
this tutorial will explain how to set up both the server, to receive message from a remote client, and the client to emit messages to a syslogd server.