At the Passover seder, those children who are still awake after the meal watch eagerly to see if the prophet Elijah comes to drink from his special cup...(and adults often shake the table to make it seem that Elijah is drinking).
At both a brit milah (circumcision, which is a covenant between God and the Jewish people - Genesis 17) and the seder, there is a special spot for Elijah. What is the connection between Passover and brit milah?
The seder commemorates the Paschal lamb (Exodus 12:3-14, 43-50), whose blood was used as a sign to God to "pass over" the Jewish homes during the plague of the first born. Similarly, the covenant between God and Abraham was sealed with the blood of circumcision. The Paschal sacrifice is the only sacrifice that may not be eaten by a man who has not had a brit milah (Exodus 12:48).
Elijah “appears” at these two ceremonies because, ultimately, he will be the harbinger of the Messianic age. But in order to bring the Messiah, the Jews must be true to their faith...and no rituals are more definitive of Jewish life than the brit milah and the seder (when the miracles God performed for the Jewish people are remembered).
Elijah’s role is that of the loving rebuker. He loved the Jews so much that he could not abide their misdeeds. He railed at their idol worship and their abandonment of the covenant of circumcision. He wanted nothing to do with them until they repented (Kings I 19:10). Therefore, Elijah now appears at each brit milah to honor those who are maintaining the covenant, and at each seder, to remind us of the promise of redemption.