Full color or four color process is printing is used when a "full" color image is required. The process involves separating an image into its four component colors (cyan, magenta, yellow and black). Once separated the image is printed using these colored inks. The four ink colors used with varying values "intensities" can then be combined to produce millions of colors.
This process is not readily applicable to lanyard material since it's best suited for printing on vinyl. Retractable lanyards which make use of plastic badge reels are typically printed using this method. White adhesive vinyl is printed, cut to the correct shape and applied to the center of the badge reel.
The advantage of this method is that the imprinted vinyl is both weather and scratch resistant. Clear synthetic covers "domes" are sometimes applied over the imprints, but this is more for aesthetic reasons than for imprint protection.