Servers are all well and good when they work, but we don't live in a perfect world, and it's perfectly possible that problems can occur (either through bad code, created by humans, or mismanagement, introduced by humans).
In theory, it would be great to simply install the program you want, set it running, and forget about it, but this is the real world, not some fantasy land where everything goes 100 percent right 100 percent of the time. This is where logging and monitoring shine.
Logging is there so that when something does, inevitably, go wrong, you don't have to keep your program in a broken state while you try and work out what's broken (though, on odd occasions, this might be precisely what you have to do; more about that later). You can bring your system back online, and start to parse the log files to find out precisely why your web server...