“From the very beginning, however, one was not unprepared in this domain to come upon failure of the forms of perception adapted to our ordinary sense impressions.” 
Here, this domain refers to the atomic theory and Bohr admits that he was not unprepared for the alleged failure of the forms of perception. What could have lead one to be prepared for this? Philosophy.
“There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.” 
So, in other words, we cannot know physical reality, only abstract descriptions. Physics is not the study of reality as it is, but simply a pragmatic description that explains what we observe.
An abstract description of what? The next quote gives us a clue.
“We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections.” 
Here Bohr means that language can not be used as a precise method of the description of reality. The purpose of words, of concepts, of ideas is not to describe reality, but to describe and relate “images” and “mental connections”.
In other words, the purpose of language, of concepts, is not to study physical reality, but to study and relate abstractions.
So when we asked, “An abstract description of what?” Of, what? Nothing? Or perhaps abstract descriptions of sense perceptions. But sense perceptions of what? We shall return to this in a little bit.
Are these abstractions to be considered objective? Bohr does not think so.
“I consider those developments in physics during the last decades, which have shown how problematical such concepts as objective and subjective are, a great liberation of thought.” 
Bohr does not consider it worthwhile discussing whether or not an idea is objective or subjective. This is not too surprising given that one of Bohr’s many philosophical influences was, as we shall see, pragmatism.