What does the baked egg mean during the Passover seder?

Answer 1

Beitzah - A hard-boiled egg (which is then burnt on one side), symbolizes the korban chagigah (festival sacrifice) that was offered in the Temple in Jerusalem and roasted and eaten as part of the meal on Seder night. Although both the Pesach sacrifice and the chagigah were meat-offerings, the chagigah is commemorated by an egg, a symbol of mourning.

More about the Seder

Pesach (Passover) is important to us since in it we relive the Exodus from Egypt and our birth as a nation, both of which were preparations for receiving the Torah from God.
The highlight of Passover is the Seder meal. This meal is of great importance in Judaism. It is a 3325-year old continuous tradition that began on the night of the Exodus from Egypt (see Exodus chapter 12), and is fully detailed in our ancient Oral Traditions (Talmud, chapter Arvei Pesachim).
The Seder meal is one of those occasions, like Yom Kippur and Hanukkah, that Jews all over the world, Orthodox and non-Orthodox alike, observe in common. During the Seder, we keep the essential mitzva and customs of handing Jewish traditions down to the next generation, with the traditional Seder foods and the ceremony of reading the Passover Haggadah which retells the events of the Exodus.
During the Seder meal, other traditional foods are eaten in addition to the matzah: bitter herbs, parsley, wine and haroset (see below). Salt water, a roasted egg, and a bit of roasted meat are also on the table.
During all the days of Passover, matzah (unleavened bread) is eaten; while leavened foods such as bread, cake, cookies, cereal and pasta are forbidden. This is a command in commemoration of the Exodus, when the Israelites were in a hurry to leave Egypt and did not spend time waiting for their dough to leaven (to rise). Exodus ch.12. Certain prayers are added in the synagogue services, and the Torah is read each day of Passover.
Here is the symbolism of the items on the Seder table:

• Matzah - this represents the haste in which the Israelites prepared to leave Egypt.
• Wine - the four cups represent the four expressions of redemption in Exodus 6:6-7.
• The bitter herbs (maror) symbolize the harsh slavery which the Israelites suffered in Egypt. Horseradish and/or romaine lettuce are traditionally used for maror.
  
• Salt water (see below).
• Charoset - A sweet mixture representing the mortar used by the Jewish slaves to build the storehouses of Egypt. In Ashkenazi Jewish homes, charoset is traditionally made from chopped nuts, grated apples, cinnamon, and sweet red wine.
  
• Karpas - A vegetable other than bitter herbs, traditionally parsley, which is dipped into salt water at the beginning of the Seder. The dipping of a simple herb into salt water (which represents tears) recalls the pain felt by the Israelite slaves in Egypt.
  
• Z'roa - A roasted lamb or goat shank-bone, chicken wing, or chicken neck; symbolizing the korban Pesach (Pesach sacrifice), which was a lamb that was offered in the Temple in Jerusalem, then roasted and eaten as part of the meal on Seder night.
• Beitzah - A hard-boiled egg (which is then burnt on one side), symbolizing the korban chagigah (festival sacrifice) that was offered in the Temple in Jerusalem and roasted and eaten as part of the meal on Seder night. Although both the Pesach sacrifice and the chagigah were meat-offerings, the chagigah is commemorated by an egg, a symbol of mourning.
  

Answer 2

The baked egg on the Passover seder plate symbolizes mourning and the cycle of life. It is a traditional food included as a reminder of the destruction of the Second Temple in Jerusalem. The egg is typically hard-boiled and represents the circle of life and the idea of rebirth and renewal.