The pomegranate is one of the Seven Species mentioned in the Hebrew Bible as being native to the Land of Israel.
The seeds of the pomegranate symbolize the 613 mitzvot (sacred obligations) attributed to the Torah (the first five books of the Hebrew Bible), which form the foundation of traditional Jewish practice.
The abundance of seeds in the pomegranate also symbolizes fertility. Many Jewish families serve the fruit on Rosh HaShanah (the Jewish new year) in the hope that the coming year will bring many blessings, much prosperity, and the opportunity to do good deeds.
Jewish families who observe two days of Rosh HaShanah often serve a pomegranate on the second night and recite the Shehecheyanu blessing to celebrate eating the first seasonal in the new year.
Additional links:
Pomegranate Orange Chicken Blessing for the Apples and Honey
