A phrase from the song, "Surfin' Bird" sung by The Trashmen in 1963.
The Bird = Extending the middle finger and "flipping someone off." Sign language for, "Fuck You!"
The "Word" = Originated in U.S. Prisons. Original meaning was, "my word is my bond", shortened to, "Word", meaning to, "speak the truth". See: Stephen Colberts segment on his show, "The Word".
Bird is the Word = Fuck You! Is the truth!
"I hear that the government may have to start drafting people again because they don't have enough people enlisting."
"Yea, if they knock on my door I will explain to them that, "The Bird is the Word". Fuck them and their military!"