Computer cluster is built of many compute nodes connected by fast communication network, such as Infiniband. Most of currently used supercomputers in the world is built on a cluster architecture, mainly due to a very good relation between price and compute power.
Clusters are great for large distributed computing, where individual application processes don't share memory directly and the problem of communication between them is solved by messages passing mechanisms, such as MPI. Most of modern scientific applications successfully use computer clusters and their scalling is reduced to a simple modification of the program startup options.
In Cyfronet there are currently two supercomputers based on this architecture: