John Lennon, who was the main writer of the song with McCartney as co-writer, said to Playboy in 1980 that it was about an affair he was having: “I always had some kind of affair going, so I was trying to be sophisticated in writing in such a smoke-screen way that you couldn't tell.” When asked about the title itself, he answered: “I don't know how the hell I got to 'Norwegian Wood'"
Sir Paul McCartney: “John told Playboy Magazine that he hadn't the faintest idea where the title came from but I do.
“Peter Asher (of Peter and Gordon, brother of Jane Asher and roommate of McCartney in their house) had his room done out in a wood, a lot of people were then decorating their places in wood, Norwegian wood.
“It was pine really, cheap pine. But it's not as good a title, “Cheap Pine, Baby"…
(Source of McCartney's quote: Many Years From Now, Barry Miles)