The year 2012 is a "Leap Year," containing 366 days instead of the usual 365 of a common year, achieved by the insertion of an additional day in the month of February (February 29), a convention which has given rise to all kinds of quirky traditions since it was instituted, such as the idea (not as common any more) that the roles of the sexes in proposing marriage should be reversed on this odd day, and the fact that babies born on this day have a sort of dual-status for their birthday and age.

The insertion of a Leap Year day is necessitated by the fact that earth's daily rotation (which creates the measure of time known as a day) does not match up exactly with earth's annual orbit (which creates the measure of time known as a year). In other words, earth's spinning on its axis as it goes around the sun happens more than exactly 365 times before returning to the exact same spot on its orbital path.

If the earth rotated exactly 365 times and came back to an identical spot, then a calendar of 365 days would mean that any successive January 1 would bring it back to an identical point on its orbit, as would any successive March 21, June 21, September 22, or December 21 (the days on the calendar that generally fall near the time earth passes through its solstice points and equinox points). Because earth rotates faster than 365 times per year, if the calendar of days were left at a simple 365 per year, the equinoxes would begin to gradually drift through the year, until spring equinox was taking place on a calendar day associated with winter (for example).

If earth's rotation were exactly 365 and a quarter turns per orbit, then the insertion of an extra day in the calendar every four years would "pull" the calendar back into alignment with the orbit quite nicely. However, earth's spinning is not quite 365 and a quarter days (or 365.25 days) in one orbit -- the actual number is just below 365.25 at about 365.24237 days per year. Therefore, the convention is that leap year days are not inserted every hundred years, on years ending in two zeros. However, years ending in two zeros which are able to be evenly divided by 400 (such as the year 2000 and the year 2400, but not the year 1900 or the year 2100) do get a leap year.

There is some analysis which suggests that in ancient times the earth rotated an even 360 times per year. Dr. Walt Brown, the creator of the hydroplate theory, points out that Immanuel Velikovsky demonstrated references to a 360-day year among the writings of the ancient "Persians, Egyptians, Chinese, Chaldeans, Assyrians, Babylonians, Incas, Hebrews, Greeks, Hindus, Romans, Aztecs, Mayas, and Peruvians" (see footnote 32 on this page of the online version of Dr. Brown's book).

He also notes that in the Hebrew Scriptures describing the flood of Genesis, the duration of the flood appears to be referred to as an even "five months" which is also described as "150 days" (see Genesis 7:11, 7:24, and 8:3-8:4). Dr. Brown believes that the events surrounding the cataclysmic flood could have increased the spin rate of the earth (just as major earthquakes continue to do to this day -- see this previous post and the figure-skater analogy).

In the description of the Isis and Osiris series, the historian and initiate into certain ancient mystery schools Plutarch (46 AD - 120 AD) relates the Egyptian myth that the god Thoth (Plutarch calls him Hermes) won an additional five days to add to the 360-day year by playing draughts against the moon deity. He writes:
They say that the Sun, when he became aware of Rhea's intercourse with Cronus, invoked a curse upon her that she should not give birth to a child in any month or year; but Hermes, being enamoured of the goddess, consorted with her. Later, playing at draughts with the moon, he won from her the seventieth part of each of her periods of illumination, and from all the winnings he composed five days, and intercalated them as an addition to the three hundred and sixty days. The Egyptians even now call these five days intercalated and celebrate them as the birthdays of the gods. They relate that on the first of these days Osiris was born, and at the hour of his birth a voice issued forth saying, "The Lord of All advances to the light." But some relate that a certain Pamyles, while he was drawing water in Thebes, heard a voice issuing from the shrine of Zeus, which bade him proclaim with a loud voice that a mighty and beneficent king, Osiris, had been born; and for this Cronus entrusted to him the child Osiris, which he brought up. It is in his honour that the festival of Pamylia is celebrated, a festival which resembles the phallic processions. On the second of these days Arueris was born whom they call Apollo, and some call him also the elder Horus. On the third day Typhon was born, but not in due season or manner, but with a blow he broke through his mother's side and leapt forth. On the fourth day Isis was born in the regions that are ever moist; and on the fifth Nephthys, to whom they give the name of Finality and the name of AphroditĂȘ, and some also the name of Victory. There is also a tradition that Osiris and Arueris were sprung from the Sun, Isis from Hermes, and Typhon and Nephthys from Cronus. For this reason the kings considered the third of the intercalated days as inauspicious, and transacted no business on that day, nor did they give any attention to their bodies until nightfall. They relate, moreover, that Nephthys became the wife of Typhon; but Isis and Osiris were enamoured of each other and consorted together in the darkness of the womb before their birth. Some say that Arueris came from this union and was called the elder Horus by the Egyptians, but Apollo by the Greeks.
Here is another website which presents some different analysis arguing that earth's year was once 360 days.

The hydroplate theory certainly does not stand or fall on the possibility of the earth once moving around the sun concurrent with exactly 360 revolutions rather than today's 365.24237. However, it is an interesting concept to consider, especially during a Leap Year.