Frame Relay was one of the earliest Virtual Private Network (VPN) technologies used to connect customer sites together to transfer data to each other. Not anymore … MPLS has jumped to the forefront as the solution of choice today.
With FR (frame relay) customer sites connect to a network provider's Frame Relay "cloud", commonly using leased line technology (64kbps – 2Mbps are common in the UK).
Once all of the customer sites are connected to the same Frame Relay cloud, the customer network is created in software using "virtual circuits". Each VC goes from the branch, to the head office or where the data application is hosted. You can create a VC for data and a separate VC for voice, each with separate performance characteristics (committed information rates).
Key things about Frame Relay – it was not very scalable and was expensive to manage (because of all the virtual circuits and back up virtual circuits). It would naturally be used to create "hub-spoke" networks with one main office and lots of little ones – which suited some businesses – even to this day. However the increase in traffic seen in customer networks throughout the 1990s and beyond has largely rendered Frame Relay obsolete.
However there are still a rump of businesses still using FR in the UK – particularly those with thin client or terminal applications with very low traffic demands, but high uptime requirements. Because access to the FR cloud was based on highly reliable leased lines, FR networks tend to be solid and unremarkable, albeit "low" bandwidth by modern standards.
In the US … that's not so true. Frame Relay is rarely even discussed when looking into new networks or upgrading existing ones.
Frame Relay competed against ATM in the late 80s and early 90s, but has been superceded by MPLS (Multi-Protocal Label Switching) and Ethernet-based wide-area networks since then. For what you once considered Frame Relay for (application) … look instead to MPLS first. If more bandwidth or robustness is needed … and cost is an obstacle … gravitate toward an ethernet based WAN. Either way you're better off than the old Frame relay.