Found very interesting!
Q. One of the reasons that we cover the Shabbos challos is to remember the mon (manna) which was surrounded on the top and bottom with a layer of dew. The Bi’ur Halachah (Siman 242) asks, why do we make a remembrance for the mon on Shabbos when the mon did not fall on Shabbos?
A. Tosfos (Pesachim 100b) writes that the purpose of covering the challah is to remind us of the mon, and when we remember the mon, we are reminded that the mon did not fall on Shabbos. (Some explanation is needed why we wish to recall the absence of mon on Shabbos. Possibly, it helps us appreciate the elevated level of kedusha on Shabbos, that even the heavenly mon was suspended on Shabbos.)
The Bi’ur Halachah offers another reason to remember the mon, even though it did not fall on Shabbos. He explains that since Shabbos is a semblance of the world to come, the foods that we prepare for Shabbos are meant to remind us of the “meal” that Hashem will prepare for tzadikim in the world to come. We eat fish to correspond to the Leviathan (some type of large fish), meat to correspond to the Shor Habar—the “wild ox” (both are foods of the messianic meal), and challos are covered like mon to correspond to the mon that will be served to tzadikim in the world to come.