When drinking the four cups of wine, and eating the matzot, the korech sandwich, and the afikoman, one is required to recline on a couch, an armchair, or on pillows. This is how royalty and nobility used to eat and on this night the people of Israel are entitled to conduct themselves like royalty.
Maimonides writes: One is required to see himself as if he had just now left Egyptian slavery. Hence, when a person eats on this night, he is required to eat and drink while reclining, as a sign of freedom.
In his commentary to the Mishnah in Pesachim, Maimonides adds: In the manner that kings and important people eat.
When reclining, one should lean to the left, eating and drinking with the right hand. Even one who is left-handed should follow this practice.
A son may recline in the presence of his father, even though a son would normally not act in this manner in his father's presence, for on this night fathers will readily permit their children to eat in this fashion. A student eating in the presence of his teacher, however, should recline only if the teacher has explicitly permitted him to do so.
It is customary not to recline when eating maror and karpas since these elements serve to commemorate the fact that the Egyptians embittered our lives.
Concerning one who is required to recline but did not do so: Regarding matzah, he should eat another portion of matzah while reclining but should not repeat the blessings.
Regarding the four cups of wine, if he forgot to recline for the first cup [Kiddush], some authorities maintain that he must repeat Kiddush while others maintain that he need not do so.
As for the second cup, one should drink another cup but not repeat the blessing. Regarding the third and fourth cups, some authorities maintain that one must drink another cup while reclining, while others maintain that there is no need to do so.
The common practice is to drink another cup only if one forgot to recline when drinking the second cup. Similarly, if one forgot to recline when eating the afikoman, he need not eat it again.
The basis for the practice of reclining is based on the verse (Exodus, 13:18) that states: And G‑d brought the people around. The Hebrew word "to go around" is very similar to the word "to lean," and the Midrash deduces from the similarity of the two words that everyone, even the most humble or poor Jew, is required to recline at the Seder as if he were a nobleman.
It is praiseworthy to recline throughout the Seder. The requirement, however, is to recline when drinking the four cups of wine, and when eating matzah and the afikoman.
Although it is no longer customary to eat while reclining, our Sages decided to continue the practice, for it serves as an additional means of publicizing the great miracle of our redemption from slavery to freedom that we celebrate at the Seder.
It is especially fitting to celebrate the Seder with guests, for the Passover sacrifice, which our Seder commemorates, was eaten in groups. Moreover, the practice of inviting guests is an additional means of indicating our status as free men.
It is customary that the person leading the Seder not pour his own cup of wine or the water that he uses for washing before karpas and eating matzah. Rather, someone else does this for him, another means of demonstrating our status as free men and nobles on this night.