The open source monitoring Icinga Server is a popular system that many people now use. Its real value lies in the way it allows you to monitor your network effectively. It does this by checking hosts and services and then letting you know their status. This naturally allows you to keep an eye on your network and find out quickly about any potential issues.
The first method sees services that are publicly available monitored. This refers to any services that are accessible via the local network or internet. This can be anything from mail to HTTP or SSH. Many people will use this to monitor systems that you don't want to put a remote agent on or user facing network interfaces.
The second monitoring method sees you install an NRPE as an agent on remote hosts to monitor their resources. This then sends back valuable information to Icinga on things like disk usage. The benefit of this is that the first method cannot achieve any of these specific tasks.