Let's say your data center is filled with Linux servers and you need to administer them all. Part of that administration job is viewing log files. But if you're looking at numerous machines, that means logging into each machine individually, reading log files, and then moving onto the next. Depending upon how many machines you have, that can take a large chunk of time from your day.
Or, you could set up a single Linux machine to collect those logs. That would make your day considerably more efficient. To do this, you could opt for a number of different system, one of which is syslog-ng.