Rosh Hashanah, even in Israel, has two nights (and days) of holiday. Each of the nights, aside for all the delicious festive foods, has a specific type of food addition.
FIRST NIGHT: SYMBOLIC
The most famous of the symbolic foods is apple dipped in honey. We also dip the Challah in honey. This is to symbolize our hopes and wishes for a Sweet New Year. We also eat pomegranates, which are loaded with seeds, to symbolize our hopes that we be filled with mitzvot and merits like a pomegranate is full of seeds. There’s custom to eat beets and leeks because of their names in Aramaic (language of the Talmud) meaning cutting away our sins. Some eat from the head of a fish, so that we be like the head and not the tail. All these (and other customary foods) on the first night are symbolic.
These symbolic foods are eaten after Kiddush and HaMotzee, at the start of the festive meal. But after we eat the Challah.
SECOND NIGHT: EXOTIC
On the second night of Rosh Hashanah its customary to eat new and unusual fruits we haven’t yet enjoyed this season or in a long while. Our family favorites are usually dragon fruit and star fruit, lychee or rambutan (both more adventurous), and then an assortment of highly unusual fruits we find at the Asian or Indian stores (they tend to have more unusual fruits).
These new fruits are on the table for Kiddush, and they are eaten after Kiddush, before we wash for and eat the Challah. They are eaten between Kiddush and HaMotzee.