Shortly before writing "This Song," George Harrison was sued for plagiarism. He was accused of stealing the tune of "My Sweet Lord" from the old Shirelles' hit "He's So Fine."
"This Song" is a comical response to that lawsuit. George is saying sarcastically that he's had experts check out the song thoroughly, and they've assured him it doesn't violate any other songwriter's copyright, so he can safely record it without being taken to court.
In the middle, you can hear two "old ladies" (actually voiced by Neil Innes and Monty Python's Eric Idle) speculating about what oldie "This Song" was copied from (one suggests it sounds like the 4 Tops' "Sugar Pie Honey Bunch," while the other thinks it sounds like "Rescue Me").
George is trying to say, in his light-hearted way, that a song is just a song, and is supposed to be FUN... which means musicians and composers shouldn't take themselves too seriously, and shouldn't be suing each other.
