Back in the day, a prize given to readers of Marvel comics who wrote letters to the editor pointing out continuity errors or other mistakes in a given issue. The joke is that there really was no prize.

From what I remember of my youthful Marvel zombiehood, you didn't win a No-Prize just for pointing out an error; you had to come up with a retcon for the mistake at the same time. (e.g. Jean Grey hated eating vegetables as a child, so that's why she destroyed the planet of the asparagus people. -- There was no particular requirement for the retcons to make sense.)

The traditional form of the No-Prize was an empty envelope mailed to you from Marvel Comics.