

You will get a zip file called Archive.zip if more than one file was selected. If you re on a Mac, just select the files you need in the Finder and right-click and select Compress X Items. The fact tat the file is usually smaller is incidental. Compressing a file or files with zip is a good way of keeping things organized and preventing a file from getting messed up in transit. Size of file is at the very bottom of the list of your priorities, below the order of operations when putting on your shoes.

You should never concern yourself with the size of a file you are getting printed.

Since you are sending a file to a printer, I will assume the latter. Do you want to send a smaller Illustrator file (fully editable)? Do you want to send a smaller PDF file (not easily editable)? Do you want to take an existing file and compress it using other software like zip?
