apt-zip will allow you to get the packages you need using a different computer instead of downloading on the computer system you are upgrading. This can be handy if you have a slow Internet connection on that computer, but have access to another system with a fast connection. apt-zip will allow you to take advantage of the benefits of apt-get like not having to worry about getting all the dependencies. apt-get will be used to figure that out and apt-zip will transfer this info on separate media that you can carry to another computer, mount it there and run a script that will download the files. Here is how it works.
This last command writes 2 files to the media and tells you how much needs to be downloaded.
You will see a list of the packages to be installed just you see with 'apt-get upgrade' If it is a large amount, you will get the option to do the upgrade or not. Choose 'Y' and the upgrade takes place using the packages stored on the media.