Why is Elijah the Prophet invited in during the seder?

After the conclusion of the seder's Grace after Meals, there is a universally accepted custom to pour a cup of wine, the "Cup of Elijah," open the front door of the home, and recite several verses from the Psalms wherein we beseech G‑d to pour His wrath upon our persecutors and oppressors.

According to tradition, at this moment our homes are graced by the presence of Elijah the Prophet. There are multiple reasons and meanings behind this age-old tradition. Here are some of them:

Opening the Door for Elijah

1) The Torah describes the night of Passover as "leil shimurim,"1 a "guarded night." It is the night when long ago G‑d protected the Jews from the plague which slew all the Egyptian firstborn, and the night when G‑d's protection over His chosen nation is most apparent. Opening the door expresses our trust in G‑d's protection.

2) When opening the door, we take the opportunity to invite in the Prophet Elijah. Elijah is the one who visits the circumcision ceremony of every Jewish child, and testifies that the Jewish people are scrupulous regarding the mitzvah of circumcision.2 Males were only permitted to partake of the Paschal Offering if they were circumcised. Thus Elijah's comes to the seder to "testify" that all present are indeed circumcised.

Additionally, according to the Midrash, on the night prior to the Exodus, the seder night, the entire Jewish male population circumcised themselves -- in order to be eligible to eat from the Paschal Lamb. Thus the clear connection between circumcision, and Elijah, and Passover Eve.

Cup of Elijah

1) There is an open question in the Talmud whether we are obligated to have four or five cups on the night of Passover. Since the issue was never resolved, we pour a fifth cup, but do not drink it.

After heralding the coming of the Messiah, one of Elijah's tasks will be to resolve all hitherto unanswered halachic questions. Thus this fifth cup whose status is in doubt is dubbed "Elijah's Cup," in anticipation of the insight he will shed on the matter.

2) The four cups correspond to the four "expressions of redemption" promised by G‑d: "I will take you out from the suffering of Egypt, and I will deliver you from their bondage; I will redeem you with an outstretched arm and with great judgments. I will take you to Myself as a nation..."3 The fifth cup corresponds to the fifth expression of redemption which comes in the following verse: "I will bring you to the Land..." This expression, however, is an allusion to the future messianic redemption which will be announced by Elijah. This is also why we do not drink, "enjoy," the fifth cup -- as we have not yet experienced this redemption.

The timing of the pouring of the "Cup of Elijah" is also apropos, right before we start reading the Hallel, whose focus is on the future redemption (see Why do we divide the Hallel into two at the Passover seder?). After commemorating the very first redemption of the Jewish people from Egypt we express our hope and firm belief in the coming of the Moshiach who will usher in the new and final redemption very very soon.

Refer to the following links for more information on these topics:

Elijah
Opening the Door for Elijah
Elijah's Cup
Four Cups

A kosher and happy Passover to you and yours!

Rabbi Naftali Silberberg,
Chabad.org