That means that instead of downloading (copying) files from CD or DVDs you have the option to only register those files in the catalog. Instead of downloading from camera or card reader, you would download 'from files and folders' and the organizer would recognize that the original media is a removeable one (CD, DVD, card, USB stick ; but not external USB drives, considered just like internal drives).
The options in this doc explain how you can avoid copying the files on your computer by only creating a small 'preview' in the catalog folder. You need to be able to insert the original media when you want not only to browse and tag the images, but to open them in the editor.
The 'offline' feature is rather a 'legacy' tool which was required when CDs were the main storing media. Remember that the organizer is nearly 20 years old.
Even if using 'offline' media is becoming rare, I think it's useful to say that if you have such files in a catalog, you'll have to 'relink' the files by plugging in the original external media. In the organizer, show the information about a given offline file, 'general' section of the information panel on the right, click on 'location' to display the dialog 'find offline Drives - Reveal in explorer'.