Rosh Hashanah meals usually include apples and honey, to symbolize a sweet new year. Various other foods with a symbolic meaning may be served, depending on local minhag ("custom"), such as cooked tongue or other meat from the head of an animal or fish (to symbolize the "head" of the year).
Foods consumed with the Yehi Ratzons vary depending on the community. Some of the symbolic foods eaten are dates, black-eyed beans, leek, spinach and gourd, all of which are mentioned in the Talmud.

Pomegranates are used in many traditions, to symbolize being fruitful like the pomegranate with its many seeds.
The use of apples and honey, symbolizing a sweet year, is a late medieval Ashkenazi addition, though it is now almost universally accepted. Typically, round challah bread is served, to symbolize the cycle of the year.

Gefilte fish and Lekach are commonly served by Ashkenazic Jews on this holiday. On the second night, new fruits are served to warrant inclusion of the shehecheyanu blessing, the saying of which would otherwise be doubtful (as the second day is part of the "long day" mentioned above).
Other symbolic foods are eaten in a special Rosh Hashanah Seder, particularly in the Sephardic and Mizrahi communities. Symbolic foods are eaten in a ceremony called the Yehi Rasones or Yehi Ratzones.
Yehi Ratzon means "May it be Your will", and is the name of the ceremony because it is traditional to eat foods symbolic of a good year and to recite a short prayer beginning with the Hebrew words "Yehi Ratson" ("May it be Your will") over each one, with the name of the food in Hebrew or Aramaic often presenting a play on words or pun in Hebrew or Aramaic. The foods eaten at this time have thus become known as "yehi ratsones".
Typical foods, often served on a large platter called a Yehi Ratson platter, eaten by modern Sephardic Jews include apples dipped in honey, or baked or sometimes in the form of a compote called mansanada; dates; pomegranates, or black eyed peas; pumpkin in the form of savory pumpkin-filled pastries called rodanchas; leeks in the form of fritters called keftedes de prasa; beets usually baked and peeled; and the head of a fish: usually a fish course with a whole fish, head intact. It is also common to symbolize a year filled with blessings by eating foods with stuffing on Rosh Hashanah such as a stuffed, roast bird or a variety of stuffed vegetables
A major significant symbol of Rosh HaShanah include the apples, honey and round loaves of challah. Apple slices dipped in honey represent our hope for a sweet new year and are traditionally accompanied by a short prayer before eating that goes: "May it by Thy will, O Lord, Our God, to grant us a year that is good and sweet." Challah, which is usually baked into braids, is shaped into round loaves of bread on Rosh HaShanah. The circular shape symbolizes the continuation of life.
On the second night of Rosh HaShanah it is customary to eat a fruit that is new to us for the season, saying the shehechiyanu blessing as we eat it to thank God for bringing us to this season. Pomegranates are a popular choice because Israel is often praised for its pomegranates and because, according to legend, pomegranates contain 613 seeds - one for each of the 613 mitzvot. Another reason for eating pomegranates on Rosh HaShanah has to do with the symbolic hope that our good deeds in the coming year will be as many as the seeds of the fruit.

from Wikipedia Judaism

Exodus 28:33–34 directed that images of pomegranates be woven onto the hem of the me'il ("robe of the ephod"), a robe worn by the Hebrew High Priest.
Kings 7:13–22 describes pomegranates depicted on the capitals of the two pillars (Jachin and Boaz) which stood in front of the temple King Solomon built in Jerusalem.
It is said that Solomon designed his coronet based on the pomegranate's "crown" (calyx).
Jewish tradition teaches that the pomegranate is a symbol for righteousness, because it is said to have 613 seeds which corresponds with the 613 mitzvot or commandments of the Torah .
For this reason and others, many Jews eat pomegranates on Rosh Hashanah.
However, the actual number of seeds varies with individual fruits.
It is also a symbol of fruitfulness.
The pomegranate is one of the few images which appear on ancient coins of Judea as a holy symbol, and today many Torah scrolls are stored while not in use with a pair of decorative hollow silver "pomegranates" (rimmonim) placed over the two upper scroll handles.
Some Jewish scholars believe that it was the pomegranate that was the forbidden fruit of the Garden of Eden.
Pomegranate is one of the Seven Species (Hebrew: שבעת המינים, Shiv'at Ha-Minim), the types of fruits and grains enumerated in the Hebrew Bible (Deuteronomy 8:8) as being special products of the Land of Israel.