JPEG uses a "lossy" compression algorithm. That means that every time you use JPEG to compress a file (not just copy, move, or rotate but actually open, change, and resave it), it will lose some image quality. ZIP uses "lossless" compression algorithms. When you zip a file and unzip it, the result is exactly the same as the file that you started with. So feel free to zip, copy, and unzip your JPEG files as much as you want.
Here's a bit of a mental puzzle. If you take all possible files of a given size and ZIP them, most of them will get larger rather than smaller. If that doesn't sound right, think about for a while.