Actually, Frame Relay is a packet switched network, as are X.25 and ATM. Ethernet is a LAN technology, and when we're talking packet vs. circuit switched we're working with the WAN space and dealing with telcos, not our local LAN.
The classic circuit switched network is the phone system. When data (in this case your voice) needs to be transmitted, a physical circuit is established between the two endpoints. When you hang up the phone, that circuit is disconnected and eliminated. In CISCO terms, circuit switched networks are great when you need guaranteed bandwidth over intermittent periods of time. Examples are: Telephone, 56k, ISDN.
Frame is the most popular packet switched network. It works by creating a virtual circuit between the two endpoints. What this means is that you only have a physical circuit between your router and the telco/isp. Once your packets arrive at the telco they are switched through various Frame Relay switches on-route to their destination. Advantages of packet switched networks are lower costs (for both the telco and for you). They're used in particular for point-to-multipoint links (branch offices to home office).