Cluster computing is basically a collection of multiple computers, storage devices and other hardware, which is represented as a single system. This means that, although there are multiple systems available, it appears as one single system to the outer world. These systems are normally connected to each other trough a very fast Local Area Network(LAN). Each computer in the cluster runs its own independent operating system.
This can be used to archive great performance and availability, as compared to a single computer. Although using multiple computers and other hardware seems very expensive, but is much more cost effective as compared to a single system of equivalent performance.
The basic concept is to get high computing power and reliability out of multiple low cost systems.