Frame Relay has been around for quite awhile, and has been challenged by the faster ATM protocol, and the ever-popular IP suite. Nevertheless, it remains one of the most popular data transmission services today. It's roots are based on X.25 and ISDN. It allows end-to-end connectivity for customer sites, and offers nationwide coverage. It is attractive for carriers because the backbone is shared - the data is carried within "frames", which are multiplexed by switches along with other customer's data. This sharing is a boon for the vendor, and also allows lower rates to be charged to the customer.
Frame Relay's most popular application is connecting remote LAN's together, but is also used for long-distance SNA connectivity. It replaces private lines for both applications.
These pages provide a complete understanding of Frame Relay - both an overview and the details.