There are two types of fruits eaten on Rosh Hashanah.
1) On the first night we eat foods and fruits that have special symbolism or association: Apple dipped in honey for a sweet new year, pomegranates so that our good deeds and merits be plentiful, a head of a fish so that we be heads and not tails and so on…
2) On the second night of Rosh Hashanah we eat a new fruit. This fruit isn’t about symbolism as much as it is about it being new for the season, different and unusual, not the regular typical. The new fruit is set on the table for both candlelighting and Kiddush so that a Shehechiyanu blessing can be recited.
There’s a technical halachic reason why the new fruit is needed specifically on Rosh Hashanah: It is the one holiday that both Israel and the diaspora observe for two days, and there’s a halachic dilemma if these two days of Rosh Hashanah are considered two separate days or “one long halachic day”. Since we recite a Shehchiyanu blessing at candlelighting and Kiddush both nights, its helpful to have the new fruit out on the 2nd night, so that it resolves the Shehechiyanu dilemma if we’re considering Rosh Hashanah one long continuous day.
But there’s more at play here, too. Rosh Hashanah is the start of a new year, and a new fruit, something different, is a symbolic way to demonstrate that. On Rosh Hashanah we start fresh! It’s not same old!
Perhaps it’s also a reminder to us to try something new, to take things to the next level, expanding our palate and horizons.
There’s an alumni family that has a longstanding tradition to seek out and purchase some of these new and exotic fruits for us each Rosh Hashanah. It’s kind of a thrill for them to find something unusual, weirder and more different than the years past. This isn’t about good taste, it’s more about the experience, and about making YomTov special.
It’s a little more challenging nowadays to get Shehechiyanu fruit, since we’re no longer limited to fruit from a local growing season. Supermarkets today regularly carry fruit from all over the world, shipped globally from seasons and hemispheres opposite our own, The Talmud considered King Solomon to be so rich that fruit was never out of season at his table, but nowadays many of us have this same availability!
So we and/or this alumni family (who also have students at UAlbany who have taken on this tradition) scour Asian and Indian stores for dragon-fruits and persimmons, asian pears and prickly pear Sabra fruit, lychees and ramboutans and other such fruit that most people don’t typically eat. And its a fun tasting tradition each Rosh Hashanah on the second night.