There's no real purpose or secret, but it's good if you have full pockets and need to pick something up. Instead of dumping something on the ground, you can eat a piece of fruit you're carrying to make room. My favorite to eat is probably apples.
Tomodachi Life Blog & QR Codes: http://www.jvgs.net/tlblog/
If you eat 7 cherries on a Friday evening and then plant a tree, a secret hatch opens. If you go down in the hatch, all of the villagers in your town are waiting for you. One by one, the villagers will give you an item from the secret 'rainbow' set. These can't be sold, but putting theem in your house makes an eternal rainbow in the sky.
*pats self on back*
that was totally fake okay
Pourquoi tu gaches ta vie?
Yep, there isn't really anything too special about eating fruit. I also like eating peaches because, well, I enjoy eating them in real life too.
Additionally, your character "blushes" or "dances" when eating a different type of food other than fruit. I'm not certain on which food produces which emotions, but I do know that the foods that produce these emotions are: cakes and chocolate hearts. I'm unsure if candy produces an emotion or if there are any other foods, but I bet someone else can confirm this.
I usually have a small orchard of my towns natural fruit just so my player can eat them. I usually have my player eat one for breakfast, lunch, and dinner. There's no need i simply like to. I always found it a bit odd that the playable characters don't seem to need to eat. The townies eat.