When you make a phone call, a dedicated connection is created between you and the receiver. This is called circuit switching. This is fine for telephone calls, but there could never be enough lines for all the billions of people sending data across the internet.
This is where packet switching comes in.
Suppose you want to send a 3MB file via the internet. The file is broken into data 'packets' of around 512 bytes. Each packet is given a header containing:
Packets are then sent to their destination along different routes, and reassembled in the right order when they arrive.