Programs like WinZip can produce things called compressed zipped files.
Basically they are useful for bundling up a number of files in one single "zip" file if you want to perhaps send them to someone or make them available to download from the internet. As well as packing them up into a single file they also try and compress each file to make it smaller.
So supposing you are a software company who has written a program that consists of say 20 assorted files. Rather than getting your customers to download the 20 files individually you "pack" them all up into a single file using a program like WinZip (there are others).
When the customer downloads this zip file they "unpack" or "extract" it into the individual files so it is then ready to install.
There are a number of similar technologies that do a simliar job and winRAR is another one, but it produces RAR files not ZIP files.
I believe Windows has the technology built in to make and extract zip files. You just right click on the file and choose extract, or one of its variants.
You can use zip files to store files on your computer, it makes it easy to keep together all files of a particular type - maybe all the photos of your holiday so you dont accidentally delete one. Or keep a spare "zip" version of your photos in case you ever delete the originals.
Yes you can send ZIP or RAR files to anther person via email, though if the ZIP or RAR file gets too big your email system may reject it.