I was wondering that too!
I think it has to have something to do with rebirth. But in an ironic way? Butterflies represent rebirth because they start as caterpillars, "die" in their cocoons, and emerge days later as a butterfly.
That's what Nat and Martha were trying to fake with Samson pretending to be Wicks resurrected.
Nat's house is a twisted cocoon, a place where Wick's body was supposed to turn to gloop (like a real cocoon) so that his reborn body could live forever as a legend.
There are butterflies on the walls, but they're all dead, pinned there forever. The pictures get smashed and destroy as Nat died and was put in the acid, destroyed by his own cocoon.
I also think the butterflies on the mugs when he tries to poison Martha are significant. Perhaps he thought that moment was going to be his transformation, his rebirth.
He would kill Martha, keep the jewel, become rich and get his wife back. He would transform from his ugly caterpillar life to a beautiful butterfly through that jewel and the poison in those butterfly cups.
But it's twisted again. He is poisoned by his own ambitions and dies a caterpillar in his acid cocoon.
I don't know if there's more that can be picked up from a closer watched, I've only seen it once. (Isn't there a picture of a child near his phone? What does that imply? Sometimes people use butterflies to represent dead children, is that part of this? Who started the butterfly theme? Him or his wife? That would also be significant). But these are my initial thoughts.
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