Chances are, unless you have some sort of fruit tree or vine in your
yard, you probably haven't been able to enjoy this phenomenon. Let's have a quick look through pictures from my peach tree. With the exception of the last picture, these were all taken on the same day, of flowers in different stages on the tree.
Maybe this sounds a bit science-class for you.
But I promise you, it's pretty cool.
(also, if you have young children of the question-asking age, it might end up being convenient)
Here's the pollenated peach blossom. I'll give you a few of the terms associated with each picture, but you can get the gist of what's happening just by the pictures.
After the flower has been pollenated, it sheds its petals. Only the stamen (red sticky-outy things) and pistil (tiny light green sticky-outy thing in the middle) are left. The pistil, consisting of the stigma, style, and ovary, is what will become the peach.
Here's a little better view of the pistil on the left. And on the right you can see where the stamen has completely wilted away. (Sorry for the blurry shots)
The pistil begins to plump up and hits the last stage of its delicious journey to peach-hood.
And voila! This was taken 2 or 3 weeks later of the same peach. These babies are almost ready to pick. The trees are still only about 3 years old, so there won't be a full harvest yet, but by next year or the following I should be up to my ears in lots of fruit things!
So that's where fruit comes from: the pistil, or center of the blossom. I hope you'll be better able to enjoy your next peach, knowing and understanding its origins. Good on you, mate.