In Chapter 1069 Vegapunk reveals that “the desires of all things are born in the world”, and that Devil Fruits are in the same boat. He says that Devil Fruits are the embodiment of what people wish they could become, and the reason why the sea, which he calls the “mother of all nature”, makes Devil Fruit users unable to swim is because it considers these wishes to transcend the world people wish to live in as “abnormalities”.
Oda literally told us the same in his interview with China Times in 2014. About the idea behind the Devil Fruits that appear in the series, Oda said he was influenced a lot as a kid by the series Doraemon and thus that most of his inspiration comes from his everyday life.
There are inspirations from his daily life everywhere. For example, because Oda often works alone all night in order to make his deadlines, he says that he would love to have the same ability as Nico Robin. If he were in possession of the Flower Flower Devil Fruit he would be able to use multiple hands at once and finish his work faster.
As for Luffy’s Gum Gum Devil Fruit, the idea came from Oda’s own laziness: he often wishes his hands could stretch out very far, like rubber, so he’d be able to get stuff without leaving his chair when he’s busy working on something.
The powers used by female characters in the series, are related to the wishes of the everyday woman. Alvida’s Slip Slip Devil Fruit gives her body the power to be slippery giving her a perfect skin. As for Miss Valentine’s Kilo Kilo Devil Fruit, it gives her the ability to change her body weight at will going from a “stout” bodyweight to becoming light as a feather making it even possible for her to fly.