Gathered from various sources:
Humpty Dumpty was a common "nickname" for people of large proportions in the 1400's. This rhyme refers to King Richard III of England. The Battle of Bosworth took place on 22nd August 1485. It was the fight for the throne between King Richard III and the head of the house of Lancaster, Henry Tudor. Richard sat on his horse atop Ambion Hill ready for battle, directing his armies when he was murdered. : "Humpty Dumpty referred to King Richard III, the hunchbacked monarch. At the Battle of Bosworth Field, he fell from his steed, a horse he had named 'Wall' (as dramatically rendered in Shakespeare's play Richard III: 'A horse! A horse! My kingdom for a horse!'). Richard was surrounded by enemy troops in the battle, and was butchered right there, his body being hacked to pieces. Hence the final part of the rhyme: 'All the King's horses and all the king's men couldn't put Humpty together again.' " This mention of Richard III is not a new idea. And the dictionary defines "Humpty Dumpty" as being a person who is short, stout, and kind of dumpy looking. If Richard had a hunchback, then he may have been called this.
Other suggested origins are that During the English Civil War (1642-49) "Humpty Dumpty" was the name for a powerful cannon mounted atop the St. Mary's Wall Church in Colchester to defend the city against siege in the summer of 1648. (Although Colchester was a Parliamentarian stronghold, it was captured by the Royalists who held it for 11 weeks.) The enemy hit the church tower and the top was blown off. "Humpty Dumpty" fell off and tumbled to the ground. The King's men tried to mend him but could not. (The "men" were the infantry, and "horses" the cavalry.)
Another suggests that "Humpty Dumpty" refers to the tale of Charles I (Humpty Dumpty) of England. He was toppled by the Puritan majority in Parliament (the great fall). The King's army (Cavaliers) could not restore his power. Charles I was executed by the Roundheads ("couldn't put back together
Since the World Book Dictionary states that "Humpty Dumpty" refers to a short, stout person this idea is very plausible.