The Egg
(יד) שָׁלֹ֣שׁ רְגָלִ֔ים תָּחֹ֥ג לִ֖י בַּשָּׁנָֽה׃ (טו) אֶת־חַ֣ג הַמַּצּוֹת֮ תִּשְׁמֹר֒ שִׁבְעַ֣ת יָמִים֩ תֹּאכַ֨ל מַצּ֜וֹת כַּֽאֲשֶׁ֣ר צִוִּיתִ֗ךָ לְמוֹעֵד֙ חֹ֣דֶשׁ הָֽאָבִ֔יב כִּי־ב֖וֹ יָצָ֣אתָ מִמִּצְרָ֑יִם וְלֹא־יֵרָא֥וּ פָנַ֖י רֵיקָֽם׃

(14) Three times a year you shall hold a festival for Me: (15) You shall observe the Feast of Unleavened Bread—eating unleavened bread for seven days as I have commanded you—at the set time in the month of Abib, for in it you went forth from Egypt; and none shall appear before Me empty-handed;

(ב) אֲפִלּוּ בְּשַׂר עֵגֶל וְעוֹף, כָּל דָּבָר שֶׁטָּעוּן שְׁחִיטָה, אָסוּר לֶאֱכֹל צָלִי בְּמָקוֹם שֶׁנָּהֲגוּ שֶׁלֹּא לֶאֱכֹל צָלִי. הַגָּה: נוֹהֲגִים בִּקְצָת מְקוֹמוֹת לֶאֱכֹל בַּסְּעֻדָּה בֵּיצִים, זֵכֶר לַאֲבֵלוּת, וְנִרְאֶה לִי הַטַּעַם מִשּׁוּם שֶׁלֵּיל תִּשְׁעָה בְּאָב נִקְבַּע בְּלֵיל פֶּסַח, וְעוֹד זֵכֶר לַחֻרְבָּן שֶׁהָיוּ מַקְרִיבִין קָרְבַּן פֶּסַח. וְיֵשׁ נוֹהֲגִין שֶׁלֹּא לֶאֱכֹל שׁוּם טִבּוּל בַּלַּיְלָה, רַק ב' טִבּוּלִים שֶׁעוֹשִׂים בַּסֵּדֶר (מַהֲרִי''ל).

16th century code of Jewish law written by Rabbi Yosef Caro

Even in regards to the meat of a calf or a bird, anything which requires Shechita (ritual slaughter) is forbidden to eat (the night of Passover) in a place where it is the custom to not eat roasted food (on the night of Passover).

Rema {Rabbi Moshe Isserles' Ashkenazic/Polish commentary on the Shulchan Arukh}

Some places have the custom to eat Eggs at their Seder, as a symbol of mourning, and I think the reason is to see that the night of Tisha B'av (which commemerates the destruction of the Temple) is rooted in the night of the Passover Seder. Furthermore, it is in remembrance of the destruction of the Temple, where we used to bring our Passover offerings. But some have the custom of not eating anything which might be dipped...

מאי שני תבשילין אמר רב הונא סילקא וארוזא רבא הוה מיהדר אסילקא וארוזא הואיל ונפיק מפומיה דרב הונא אמר רב אשי שמע מינה דרב הונא לית דחייש להא דרבי יוחנן בן נורי דתניא רבי יוחנן בן נורי אומר אורז מין דגן הוא וחייבין על חימוצו כרת ואדם יוצא בו ידי חובתו בפסח חזקיה אמר אפי' דג וביצה שעליו רב יוסף אמר צריך שני מיני בשר אחד זכר לפסח וא' זכר לחגיגה רבינא אמר אפילו גרמא ובישולא

The Gemara asks: What are these two cooked foods mentioned in the mishna? Rav Huna said: Beets and rice. The Gemara relates that Rava would seek beets and rice for his meal on Passover night, since this ruling came from Rav Huna’s mouth. Although Rava realized that Rav Huna was merely citing examples and did not mean that one must eat those specific foods, he wanted to fulfill the statement of his teacher precisely...Ḥizkiya said: The two cooked foods can even be fish and the egg that that was fried on it. Rav Yosef said: One requires two types of meat on Passover night, one in remembrance of the Paschal lamb and the other one in remembrance of the Festival peace-offering, which was also eaten on Passover night. Ravina said: For the two cooked foods one may use even the meat on the bone and the gravy in which it was cooked.

כשהיה בית-המקדש קיים היו מביאים לירושלים עם קרבן הפסח גם קרבן חגיגה; את בשר קרבן החגיגה אכלו לפני קרבן הפסח. היום אנו מניחים בקערה ביצה מבושלת, זכר לקרבן חגיגה.

יש נוהגים שלא לאכול את הזרוע ואת הביצה עד למחרת ה"סדר"; לפי מנהג אחר אוכל עורך ה"סדר" את הביצה שבקערה בליל ה"סדר" או למחר היום.

Encyclopedia Yehudit

When the Temple stood in Jerusalem, they used to bring, along with the Passover offering, a special Holiday offering. They would eat the meat of the Holiday offering before that of the Passover offering. Today we place a cook egg on our Seder plate, in remembrance of the Holiday offering.

There are some who have the custom of not eating the Shankbone or Egg until one full day after the last Seder. There is another custom that some people eat the Egg from the Seder plate on the night of the Seder itself, or the next morning.

(יא) (יא) ונ"ל הטעם וכו' - והגר"א כתב עוד טעם מפני שהביצה הוא זכר לחגיגה וכמבואר לעיל בסימן תע"ג ס"ד וע"כ צריך לאכלו ג"כ ומה שאין אוכלין הזרוע לפי שעושין אותו צלי כמ"ש בסימן תע"ג ואין אוכלין צלי ויוצאין באפיקומן שאוכלין עכ"ד ולפ"ז נראה דיהדר לאכול גם בליל א' אותה ביצה שעל הקערה ושאר ביצים שאוכלין הוא משום שנשתרבב המנהג:

The Mishnah Berurah was written by Rabbi Yisrael Meir Kagan, a 19th century Rabbi in Poland

The GRA (a late 18th century Lithuanian Rabbi) further wrote that the reason for the Egg is as a remembrance of the Holiday offering. And as it explains elsewhere, we need to eat this, as well. But we do not eat the Shankbone as it is roasted (and eating roasted things is forbidden until the Temple is rebuilt)....and we see that eating the egg on the Seder plate is a beautiful action, and any other Eggs we eat that night are simply multiplying the custom.

A Kabbalistic take on the Egg, which corresponds each letter of the name of God with a rationale behind the purpose of the Egg

yud

wisdom

egg laid by a live hen

hei

understanding

egg found in slaughtered chicken

vav

zeir anpin; the six emotive powers

egg fertilized by male bird within a distance of sixty houses

hei

kingdom

unfertilized egg produced by the hen when she is warmed by the earth

Eggs in the Talmud

Susan Weingarten

Whether eggs were actually eaten with salt water, as is traditional among many Jews today at the Passover seder meal, is unclear from [Rabbinic sources]. They were certainly eaten sprinkled with salt, as there is a discussion of whether eggs or radishes may be salted on the Sabbath...Seasoning with salt, indeed, was seen as pretty well essential when eating the eggs described as Megulgelet, or rounded.
When a fast day fell on the Sabbath eve, people would begin to celebrate the Sabbath hungry, and this was not considered desirable: the Sabbath should be enjoyed. So the rabbis allowed people to assuage their hunger with minimal food towards the end of the fast, but without enjoying it, as was proper on a day of fasting and mourning. Thus it is reported that Rabbi Aqiva sipped a megulgelet egg without salt--
eating to assuage his hunger but without being able to enjoy his egg.

Excerpt from "A Humanistic Haggadah"

BEITSAH - EGG - [Roasted egg held up for all to see.] BEITSAH Why do we have an egg on the Seder plate? The egg is a symbol of life and of the rebirth that occurs each Spring. But the egg is also fragile and so it also represents potential that can be destroyed. Growing life needs warmth and love and security, guidance, hope, and vision. Beitsah is also a symbol of the interdependent web of life.

Rabbi David Pincus commentary on the Haggadah

Gevurah - The Beitza symbolizes the Korban Chagigah. An egg is round, and closed in on all sides, which implies limitation and finite-ness, which is the idea of Gevurah, which implies strictless and limitations. So it symbolizes physical gifts, which are finite and limited. The Beitza is on the plate to remind us that even physical gifts from Hashem must be connected in our mind to their source, which is also Hashem. And we cannot only look at spiritual gifts as having a spiritual source (i.e. Hashem), but we must look at those physical gifts as well as coming from Hashem.

I was also thinking that this breakdown is interesting in another way. The Z'roah is the right side, the side of Chesed, which is the "masculine" side. And its symbol on the seder plate is the Z'roah, which is a Kav, a line, which is similar to the letter zayin, which means "zachar," male. (V'hameivin yavin.) So that's an interesting correspondance. Also, the Beitza is on the left side, and symbolizes Gevurah, which is the "femenine" side. And the Beitza is similarly an appropriate symbol for the femenine side since an egg would certainly correspond to the femine side for obvious reasons.

Ariel Pelaia, about.judaism.com

Roasted, Hard-Boiled Egg (Beitzah, ביצה): There are several interpretations of the symbolism of the roasted and hard-boiled egg. During the time of the Temple, a ​korban chagigah, or festival sacrifice, was given at the Temple and the roasted egg represents that meat offering. Also, hard boiled eggs were traditionally the first food served to mourners after a funeral, and thus the egg serves as a symbol of mourning for the loss of the two Temples (the first in 586 BCE and the second in 70 CE).

During the meal, the egg is merely symbolic, but usually, once the meal begins, people dip a hard-boiled egg in salt water as the first food of the actual meal.

The Symbolism of the Egg

Mama Lisa's Blog

The egg is also part of the Jewish Passover holiday that takes place in the Spring. The egg is placed on the Seder plate and is a symbol of sacrifice and loss. Yet to some it also symbolizes the full cycle of life, and therefore hope and rebirth. (The egg is a more recent addition to the Seder plate compared to the other symbolic items that are found there and its symbolic meaning seems to be more open to interpretation.)