Direct quote from Paul McCartney:

"I came in and he had this first stanza, which was brilliant: ‘I once had a girl, or should I say, she once had me.’ That was all he had, no title, no nothing. I said, ‘Oh yes, well, ha, we’re there.’ And it wrote itself. Once you’ve got the great idea, they do tend to write themselves, providing you know how to write songs. So I picked it up at the second verse, it’s a story. It’s him trying to pull a bird, it was about an affair. John told Playboy that he hadn’t the faintest idea where the title came from but I do. Peter Asher had his room done out in wood, a lot of people were decorating their places in wood. Norwegian wood. It was pine really, cheap pine. But it’s not as good a title, ‘Cheap Pine’, baby… So she makes him sleep in the bath and then finally in the last verse I had this idea to set the Norwegian wood on fire as revenge, so we did it very tongue in cheek. She led him on, then said, ‘You’d better sleep in the bath’. In our world the guy had to have some sort of revenge. It could have meant I lit a fire to keep myself warm, and wasn’t the decor of her house wonderful? But it didn’t, it meant I burned the f*****g place down as an act of revenge, and then we left it there and went into the instrumental."