The Talmudic rabbis could not agree if there should be four or five cups of wine based on Exodus 6. . .

Opening the door is a welcome to the spirit of the Prophet Elijah and to the hope for the best future.

אֵלִיָהוּ הַנָבִיא, אֵלִיָהוּ הַתִּשְׁבִּי, אֵלִיָהוּ הַגִלְעָדִי בִּמְהֵרָה יָבוֹא אֵלֵינוּ עִם מָשִׁיחַ בֶּן דָוִד

Elijah the Prophet, Elijah the Tishbite, Elijah the Giladite, May he soon come to us, with the Mashiach (age) the child of David.

............

Next to Elijah's cup, is Miriam's cup.

זֹאת כּוֹס מִרְיָם, כּוֹס מַיִם חַיִּים. זֵכֶר לִיצִיאַת מִצְרָיִם

Remember the righteousness of the midwives Shiphrah and Puah, of Jochebed and Miriam, and of all the women who helped to redeem us from the Narrow Places (Talmud Sotah 9b) and that Miriam's Well was the source of water for the Israelites in the desert. (Ritualwell.org)