A mobius is a twisted circle that has one surface and one edge, as explained by Cat Bordhi. A mobius cast on is a special cast on so you can knit the twisted loop. It's sort of like a provisional cast on that goes around your circular needle two times, so your needle is doubled over, and you start from the center and knit out, putting in patterns as you want.
Congrats, Merry! Any chance we'll see a pic?