Rsync, in the words of its official Web site at http://www.samba.org/rsync/, is a "faster, flexible replacement for rcp". (for those of you not clued into the lingo, rcp is a remote shell program which allows you to copy files from one host to another). Like rcp, rsync allows you to transfer files between hosts; however, unlike rcp, rsync attempts to identify differences between source and destination files prior to initiating a transfer, and (assuming differences exist) tries only to copy the changes, rather than the entire file.
Needless to say, this is far more complicated than it seems - rsync accomplishes it via a specially-designed algorithm that allows it to obtain a list of all the differences between the source and destination files, and transfer these differences only. You don't need to worry about the details - if you're really interested, you can read about rsync's internals at http://dp.samba.org/rsync/tech_report/ - but you certainly should be impressed with the end result: a substantial reduction in both bandwidth and time used, all accomplished by the simple expedient of transferring only the differences between files, rather than the entire file.
In addition to the differential-search algorithm that makes up the core of rsync, the program also comes with a bunch of other useful features. Files (and not just files, oh no - entire directories, devices and links too!) can be copied from one host to another with permissions and other file attributes intact. Support for two-way transfer substantially simplifies the task of mirroring data between hosts. Built-in authentication makes it simple to protect access to sensitive files, and data can be transmitted over SSH for greater security.
Intrigued? Wanna see it in action? Flip the page, and let's get installing!