The process of "zipping" a file refers to putting it into an archive format such as "ZIP." This compresses the file, making it smaller. You can compress several files into a single ZIP archive, making them easier to store and transfer over email as the files are smaller, and they can be moved by just moving that one ZIP file. If you need to move many files, or very large ones, then zipping them may be the best way to go.
The term "zipping" when applied to files refers to the process of compressing them into an archive. One of the reasons "zip" is the term used is that one of the most popular archive formats has the file extension "ZIP." That doesn't mean that this is the only archive format that can be "zipped," however. You can also apply that term generally to any kind of compression, including into formats like RAR or 7Z. These compression formats are used by the programs WinRAR and 7Zip.
One advantage to zipping files is for the purpose of storage and organization. If you have a great number of files that you don't plan on using any time soon, you can "zip" all of them into a single archive. This will make them smaller, and it will also organize them in one file that you can easily find and use. Some files on your computer can be very large, so condensing many of them into a single zipped file can greatly cut down on both the amount of storage you need, and any trouble you might have in locating them.
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Another advantage to zipping files is that you can more easily transfer them. A file zipped in an archive will be smaller than the original version. It will also be just one file, as you can zip many files into it. This makes emailing the zipped file as an attachment to someone else over the Internet a lot easier, especially because some email websites have a limitation for how large a file you can send through them. That means that you can email a file to someone in zipped format where you wouldn't have been able to send it to them at all otherwise.
Transfer to Media
It's also advantageous to transfer a zipped file to something like a blank CD or a USB flash drive. Because the zipped file is smaller, you can add much more to a CD than you would have been able to otherwise, and a smaller file means that the process of making the CD will take less time. If you zip all your files in this way, then you could fit a good deal more files on the CD than you would have been able to if you hadn't tried zipping them.
Examples of programs that allow you to take advantage of zipping files include WinZip and WinRAR. After you download and install such a program on your computer, you can often zip files into an archive by just right clicking on the particular file, and selecting an option offered by one of the programs to add it to a new archive. After you do this once, you can add other files to the same archive in the same way, which will allow you to take advantage of the many uses of zipped files.