The hoax began in 2003 with an email that was widely circulated, claiming that Mars would appear as big as the moon on Aug. 27 of that year. Since then, the email has been circulated every year on the same date.
That email (of ambiguous origin) corrected noted that Mars and Earth would be at their closest distance since 57,617 B.C. on Aug. 27, 2003. That year, on that date, they were separated by 34.6 million miles. Compare that to their average separation of 140 million miles and indeed, they were really, really near in astronomical terms.
The email then correctly went on to state that Mars "will attain a magnitude of -2.9 and will appear 25.11 arc seconds wide." Then, the confusion came in. It doesn't appear that the intent was to confuse, but the sentence in the email was worded in such a way that confusion was easy. It said:
"At a modest 75-power magnification Mars will look as large as the full moon to the naked eye." Close-up pictures of Mars and the full moon side-by-side accompanied the text.
It would be easy for a speed reader to miss the fact that in order for Mars and the moon to appear the same size, Mars would need to be magnified 75 times versus the naked eye.
Wikipedia actually has the email text in full, including the line breaks that appeared in the original.
The sentence about Mars' size relative to the moon had a line break in it, and was read as such:
"At a modest 75-power magnification
Mars will look as large as the full moon to the naked eye."
That said, Mars Hoax Day has become a tradition. To be clear, the only way that Mars could appear as large as the moon to the naked eye would be if it were about twice as far from the Earth as the moon, since Mars is about twice the size of the moon.
The moon is an average of 238,000 miles from Earth. If Mars were about 476,000 miles from Earth, the hoax would be real. Of course, if that were to happen, it would be disastrous. In 2005, NASA said the following in a statement addressing Mars Hoax Day: "If Mars did come close enough to rival the Moon, its gravity would alter Earth's orbit and raise terrible tides."