Q. What is the source for reclining while eating the Seder anyway?
A. Rambam (Chometz Umatza 7: 6,7) writes that since our Sages teach us that in every generation one has to see himself as if he actually has been saved from Mitzrayim, therefore our sages instituted that one should recline as only free men do. See similar ruling in Shulchan Aruch (O.H. 472: 2).
Some Poskim argue that reclining at meals does not apply in our days, as we don’t eat anymore in that fashion (Avi Hoezri 525 quoted by Tur 472). However most Poskim maintain that reclining still applies and one should follow the tradition.
Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit’a