Packet Switching
Data is broken down into pieces, sent to a different computer and then re-assembled on that computer. Packet switching allows files to be sent a lot faster as it is sending multiple smaller files at the same time instead of one large file.

Circuit Switching
This is where a line is established between two end-points which creates a single connection. Most common phone calls are circuit-switched. A line/path is created and locked by the telephone company when you phone someone and they answer. This lasts for the duration of the phone call. During the phone call, nobody else can use the line that you are on for the entire time.