The Great Bird of the Galaxy was a creature evoked as a blessing. In fact, it is an inside joke. As such, it has no direct analog in American English.
It term was first used by Lieutenant Hikaru Sulu in the Star Trek episode, "The Man Trap." when he said, "May the Great Bird of the Galaxy bless your planet!"
"The Great Bird of the Galaxy" was the nickname of Star Trek executive producer Gene Roddenberry, given to him by associate producer Robert Justman. It was used in the original series as an inside joke.
Appearances In Star Trek
In addition to the blessing used by Sulu, the Great Bird of the Galaxy appears on a computer display in the Star Trek: The Next Generation episode, "The Naked Now." The image was based on a full-color painting made by Andrew Probert as gift to Roddenberry on his sixty-sixth birthday.[The Bird 1] It depicts the Bird as Roddenberry's face on the body of a parrot wearing a Starfleet uniform.