The processed indicator on the cartridge means the film inside has been developed into negative images (a.k.a. "negatives"). This process only needs to be done once.
To make prints, the negatives are projected onto light-sensitive paper and the paper is developed so they become the positive prints you expect to see. Because the negatives are considered the original source material for the picture, they're returned to you so they can be used again to produce more prints or create scanned digital images.
Negatives are usually cut into short strips and returned in an envelope with your prints. The Advanced Photo System (the generic name for what Kodak called Advantix) changed that by winding the processed film back into the cartridge for safe keeping.