Daniel Ingram's take on No Dog:

No Dog is a term coined by Kenneth Folk. It is used here to describe a transjhanic state, meaning a state that remains and can have all the other jhanas and insight stages arise and vanish and not change much about the fact that one has turned one's attention to it.

As an attainment, it is very satisfying in a way that few things are. There is controversy about exactly when one may attain this, but I personally attained it very shortly after attaining arahatship. I write my take on it in an essay called No Dog, Some Dog and the Simplest Thing.