Ring Around the Rosie. Bubonic Plague.
This is about the plague of London. One of the symptoms of the disease was a red rash on the skin (a rosie ring if you will). People carried posies around in their pockets to ward off the smell of the disease, and "Ashes, Ashes, we all fall down" refers to the high mortality rate associated with the disease. (Side note: I've also heard that the phrase "In the dead of the night" refers to the plague, as people would take their dead out for collection and burial in the middle of the night.)
Georgie Peorgie. Adulterous royalty.
Georgie was George Villiers, 1st duke of Duke of Buckingham, who had an affair with the Queen of France, ruining her reputation (and making her cry because of it). Oh yeah, and he wasn't popular, which is why he ran away when the boys came out to play.
Jack be Nimble. A pirate's life is the life for me.
They say Jack is Black Jack, a notorious English pirate, who regularly escaped from the authorities (boy, was he nimble). Just to wrap this one up, they talk about candle leaping, which some English did at fairs back in ye olde medieval times(talk about starved for entertainment).
Jack Sprat. More royalty with issues.
King Charles I (Jack Sprat) declared war on Spain but Parliament wouldn't fund it (he was lean). His wife imposed an illegal war tax on the populace (to get some fat). He dissolved Parliament (licking the platter clean).
Mary, Mary, Quite Contrary. Sheesh, no wonder we rebelled. These people are a pain in the ass.
Mary is Bloody Mary Tudor. The old wench had many innocent people tortured and beheaded for failing to convert to Catholicism (Unsurprisingly, she was the daughter of King Henry VIII - talk about the head not falling far from the guillotine). The garden refers to the graveyard for non-converts, minus their craniums. Silver bells were thumbscrews, which crushed the thumb between two hard surfaces by tightening the screw. Cockleshells - again torture: look at the root of the word and you'll get an idea of what it involved. Ouch!
Of course, some say it's about Mary I of England and mocking her for her miscarriages. Her womb, or garden, was barren and that the original line was not "pretty maids all in a row" but "dead babies all in a row" (as in their little graves).
Jack & Jill. Because the French aristocracy sucked, too.
Since we're on the subject of guillotines, let's chat about Marie Antoinette and her hubby. Jack was King Louis XVI was beheaded (that's one way to lose your crown) and was then followed by Jill, or Marie Antoinette (hers came tumbling after).