If a suitcase lid won't close, you can sit on it and all the excess space and air goes out of the contents. All your long underwear gets scrunched up nice and small and then you can do up the clasps on the case. In the computer world, ZIPs are really files that have been shrunk by taking repetitions out of the binary code.
Binary code is a bunch of ones and zeroes that all files are made up of.
When you ZIP a file, you pull out all of those repetitions and replace them with markers or tokens. This is useful in telecommunications because a smaller file takes less time to transmit over the Internet or any network. So file transfers from one computer to another are quicker, because there's less data to send. You'll find word processor files and images will typically ZIP down to a fraction of their original size. Pictures are particularly crunchable.