The implication is that when the text tells us, “They drew near to God and they died”, it means that they “drew near” in an inappropriate way.
Amongst the Chassidim, however, there is a notion that what went wrong was not the normal kind of human sin but an overabundance of spiritual exuberance. They were so full of ecstasy at being in the presence of the Almighty that their bodies burst with spiritual energy and could no longer function in the regular earthly way.
One might say that they ceased to be human beings and almost rose to the disembodied heights of the angels.
The Lubavitcher Rebbe asked why the story of Nadav and Avihu is read on Yom Kippur. He answered that though Yom Kippur is or ought to be the acme of spirituality, our task is to be spiritual whilst remaining human beings and living in the world.