Switching means directing signals or data towards destination. A switch works at Data Link Layer. A switch allows different devices in a network to communicate and hence it works on Data Link Layer as it uses MAC addresses. A router on the other hand helps different networks to communicate and hence a router works upto network layer as it uses ip addressing.
Circuit vs Packet
Initially, in circuit switching, a route is defined (which is called the circuit) between the sender and receiver. When you wish to establish a virtual circuit, the first packet, as it travels allocates resources accordingly on the way for the other packets following it. The other packets follow the same path, on the route established by the first packet. It is connection-oriented.
In packet switching, the packets are just sent. They may or may not follow the same path. They will just anyhow reach destination if not lost. It is connectionless.
Which is better? Depends. In circuit switching, large amount of data can be sent faster and more reliably (As path would be established already, there would be no packet headers to each packet. Only the first packet has a global header.). Moreover, packets will be received in order. All this comes with the cost of allocation of resources in intermediate nodes. Packet switching is better when message size is small or order won't matter (Headers help in ordering anyways), etc and cheap and easy solution.
