Haki is the Power of Will. It is a tangible thing in the One Piece Universe. It can be augmented by one’s own emotion, allowing one to find strength they shouldn’t have.
It explains how Luffy was able to beat people he normally shouldn’t have been able to – it is through sheer emotion being translated to force of will i.e. Haki.
My theory is that the Devil Fruits all utilise Haki at their core, and are linked to D. Clan and the Ancient Kingdom.
It is clear that all living things possess Haki, but what is less known is that all non-living things also do – this allows Roger to ‘hear’ the poneglyphs, and Zoro to hear the rocks that fell at Alabasta.
The Devil Fruits work on the basis of the Haki of inanimate things, merging with Haki of the user, in order to create a single Will.
Now there is an old theory according to which the D stands for a smile (aka 😀), suggested by the fact that all the D’s we know died smiling, not to mention Luffy at Loguetown.
There is something about Devil Fruits that involve emotional energy, and positive emotion at that, and the D. Clan knew of this, allowing them to interact with the natural world on a level. This idea is reinforced by Joy Boy and Laugh Tale.
And the fact that Roger is almost always seen smiling, the artificial Devil Fruits are called SMILEs and faulty fruits cause one to be unable to stop Smiling.
*Theory by seedyProfessor