These sentences are confusing because the author has used the word "reason" three times, with two different meanings. It will help if we split up the ideas.
How do you explain to someone the reason for...
In this part of the sentence, the author is asking for the reader's explanation of what will come next. The word reason here can mean "cause of" or "justification for".
...the failure of reason?
In this part of the sentence, the author is talking about the failure (or loss of) reason, meaning logical thought and rationality.
Words fail, passion fails, reason fails....
The author then goes on to list other things that may fail (or be lost) - language and wit, emotions, and (again) reason meaning rational thought.
The author is describing a general loss of mental health, and the context will likely establish that this is due to illness or advanced age.
The request for an explanation is the author's way of making the reader think about the topic. Rather than describing the loss of mental health, the author asks the reader to describe it. The author hopes the reader will become more engaged, and be more likely to agree with the author's position.