This seems like a dense topic, so I'll put out my understand of it, as it is now.
We're familiar with pollination, yes? Once that occurs, the flower goes from being a flower to being fruit, which contains the seeds. In the case is a deku sprout, I believe the fruit would be the deku nut. The purpose of a fruit is sometimes to get animals to eat it, so that the seeds will be carried elsewhere by the animal and, er, deposited later.