Question

What is ironic about the fact that framton goes to the countryside to relax his nerves

Answer 1

Framton Nuttel has taken a trip into the country, at his sister's insistence, to cure a nervous condition.  Mr. Nuttel, his sister fears will remain isolated and alone if he stays at home, so she encourages him to visit the countryside.  She writes him letters of introduction, so that he can visit strangers and spend time relaxing and recovering as per his doctor's orders.

He is supposed to spend time in the country recovering from his illness, but the absolute reverse happens.  He gets more nervous and anxious, after just his first visit.