Tony Asher has explained the esoteric origins of this song:

There was an album out called How to Speak Hip […] a lampooning of the language instruction albums. I played it for Brian, and it destroyed him, killed him. Brian picked up a couple of references on the album. One of them was this hip character that said if everyone were ‘laid back and cool, then we’d have world peace.’ So Brian started going around saying, ‘Hey, would somebody get me a candy bar, and then we’ll have world peace.’. [Brian] even made an acetate disc with a label on it with the title. He talked about calling Let’s Go Away For Awhile ‘And Then We’ll Have World Peace.’"

Brian is quoted as calling this track, “the most satisfying piece of music [he] ever made.”

• Source – Pet Sounds Track Notes