Why Apples ?

Well ...

1. In kabballa, the scent of an apple orchard is said to resemble the smell of Gan Eden. ( see Rashi in Bereshis 27:27 ) therefor - we dip an apple in honey to symbolize our desire to see Hashem's kingdom declared ( as is the focus of the entire Rosh HaShana davening ) and the "scent" of Gan Eden permeate the world.
2. The apple is a traditionally sweet fruit and we dip an already sweet fruit into honey ( which is even sweeter ) to show that we are hoping for a really sweet year. Additionally, the idea of sweetening something is not just a culinary preference - rather - it refers to injecting doses of mercy into Hashem's otherwise strict judgment of us. By sweetening the year we are actually hoping to be judged favorably.
3. Shlomo Hamelech compares the Jewish people to an apple tree [Shir HaShirim 2]. The Medrash Rabba states that the apple fruit matures before the leaves on the tree can sufficiently protect it - similarly - so did bnei yisrael say "Naaseh" ( we will do the mitzvos ) before "Nishma" ( we will hear what they are ). So the apple is symbolic of our wholehearted desire to serve Hashem completely - with no reservations or conditions.

May we ( and all klal yisrael ) be zocheh to a sweet year, a year of bracha and hatzlacha - a year where we truly bring to frui(t)tion all of the symbolism of Rosh Hashana night.