Not sure which part you're not understanding, but not embedding images means they want to keep a separate file linked (if you have placed a photo or pixel-based illustration into your layout) rather than embedding it into the InDesign or Illustrator document. This probably has to do with what RIP they use in their plate making... and one file that had an embedded image back in 1993 probably gave them trouble so they say never do that again.

Flexo printing (or "Flexographic" or "Flexography") uses plates made from a thick(ish) silicone-rubber type material, and a reverse image is etched into the rubber surface. The flexible rubber plate is placed onto the printing press, and ink is applied to the plate which make it's impression onto the paper/label material. This type of printing is very widely used in the label/sticker industry (as well as the newspaper industry). In the last few years, they have solved many of the registration issues so that you can now do CMYK + spot with very nice results.