This expression came into use during the days of the U.S. space program in the 1960s. It was language used by Mission Control in the moments before a launch. The drama and real-live emotion were impressive and people picked it up. They would ask each group, department, location, etc. if they were ready for launch. It was a name for one of several possible statuses, I guess, so it was used as a noun. They would go through a sort of roll call. "Houston?" "Houston is GO!" "Cape Canaveral?" "We have a GO!" or "We're GO here!"
It is similar to saying "We have a green!" for "We have a green light" or "I got an A!" for "I got a grade of A."
The verb "go" has been transformed into a noun.
Another bit of space program talk that was popular for a decade or so but did NOT survive was "A-OK" (meaning everything is fine).
The Apollo 13 program gave us the catchphrase "Houston, we have a problem." It is used to mean a very serious problem (in the case of Apollo 13, one that put the astronauts' lives in danger) and the idea to sound like a tough test pilot or astronaut, delivering very bad news in a calm and understated way.