I seem to remember my father’s explanation going something like this…
The QB, desperate for more than three points but nowhere near scoring, with only a handful of seconds left on the clock, throws the ball in a long, high arc, aiming for the end zone. Everyone in the stadium–offense, defense, fans, the hot dog guy, even the ref–knows what’s coming, because there’s really no other choice. Normally when a defense knows what you’re going to do, you try to do something else, but in this situation, it is the only possible play, and defending against it is pretty easy. Nonetheless, the quarterback’s hand (and arm) is forced.
He throws long and high, knowing that the time left on the clock will expire no matter what kind of play is run. The massive hang time is long enough for the receivers to get downfield under his pass, long enough for the defenders to set up coverage, and long enough for the quarterback to say the complete Hail Mary prayer, to wit:
Hail Mary, full of grace. The Lord is with thee.
Blessed art thou amongst women, and blessed is the fruit of thy womb, Jesus.
Holy Mary, Mother of God, pray for us sinners, now and at the hour of our death.
Amen.
With the big game in the balance, your pass in the air, and a mob of defenders and receivers in the end zone, you may as well pray–you’re going to need it!
As for who coined it, Google gives one decent cite that it was Roger Staubach vs. the Vikings in '75. Probably not enough evidence to go on.
Aside to kanicbird: the Immaculate Reception was Franco Harris, snatching a Terry Bradshaw pass intended for “Frenchy” Fuqua from inches above the ground in the final seconds of the AFC Championship game (Steelers vs. Raiders, 1972). The “Immaculate” moniker is questionable; the play was ruled a touchdown because none of the referees could determine whether Fuqua has touched the ball, or whether it had bounced off his defender. In the latter case, it would be a valid reception; in the former, the penalty would be for “Illegal Touching” and the game would be over. It is still one of the most hotly-debated plays in (American) football.