A cluster is a group of computers which perform the same function to produce the same set of results. Each LiveJournal cluster consists of a group of web servers and database servers, and each database server in a cluster is designed to retain an identical copy of user data (such as your journal entries and user pictures) to not only reduce the amount of time it takes to obtain certain data, but also reduce the risk of data loss.
The clustering system is designed so that LiveJournal users are grouped, with each group's user data stored on a different cluster of machines. This increases site performance, as not everybody is trying to access the same database or web server; and finally, it means that not every user is inconvenienced when maintenance has to be performed on a certain cluster for whatever reason.
At any time, you can find out which cluster your data is stored on by logging in (http://www.livejournal.com/login.bml) and going to http://www.livejournal.com/misc/whereami.bml.