I've combined some Wikipedia research about the facts of the historical time with the nuances of the play. Here is my un-authoritative synopsis of the history and characters of "Richard III" by William Shakespeare:
How are Kings made? It's a game of chess.
Preface before the play: The War of the Roses
Henry VI was one year old when his king father died. He was a Lancaster.
His cousin was Richard, Duke of York. This man was also in a direct line to the throne from a previous king, Edward III - and Richard married and had 13 children. He is the father of the later kings Edward IV and Richard III. Young Richard, born 12th of the 13 children, was raised to be a military man and given significant military roles from the age of 11.
For an interlude as an adult, King Henry VI had a mental breakdown - Richard, Duke of York was then made regent. When the king regained his sanity, Richard, Duke of York became his enemy. Battles ensued between the Yorks and the Lancasters. Many of the York key defenders of this generation were subsequently killed in battle or executed.
Henry VI, married to Margaret, had a son Edward who would have been the rightful heir to the throne. They, representing the Lancasters, were significantly defeated in battle by the Yorks. Henry VI was captured and murdered in the Tower of London. This murder, according to Shakespeare, was the work of Richard III. Queen Margaret pressed on in further battles, attempting to keep the crown for her son; she was also finally defeated, perhaps also to the credit of Richard III.
The play: Richard III
In this next generation of Yorks, three sons survive and are in Shakespeare's play: Edward, George (aka Duke of Clarence), and Richard. Edward is King Edward IV.
(It is known that through their marriages the estates of Richard and George became legally entangled and so there was known cause in history for enmity between them. George, in fact but for reasons I don't know, was killed while imprisoned in the Tower.)
Richard's actual wife was Anne Neville, a close relative he'd met 12 years before; she was the widow of a man who had been a Lancaster and heir to the throne.
King Edward IV and his wife Elizabeth had two sons and a daughter. Elizabeth's clan is the Woodville family, and her brother and sons (from a previous marriage) are in the play. After the king's death, the marriage was declared invalid and the heirs illegitimate. Richard III became king; the young princes were never seen again. Their sister, Elizabeth, survived.
The Duke of Buckingham, once Richard's loyal ally, is later betrayed by Richard and becomes his foe. Buckingham then rallies Henry Tudor, who resides in exile in France, to fight against Richard. Buckingham was later captured by Richard's allies and beheaded.
The loss of Buckingham was a grave blow to Henry Tudor's campaign. However, Henry Tudor ascended for a second battle through the agencies of female support; his staunch supporters included his mother, Buckingham's widow, the Woodville family of the prior Queen Elizabeth, and the female regent currently ruling in France. After he vowed to marry the surviving daughter of Edward IV, Elizabeth, he was able to rally broad support to fight Richard's forces a second time.
With Richard's forces outnumbering those of Henry Tudor, it might have been easy for Richard to keep his crown and his life. However, there were significant defections of key allies on the battlefield.
As in the game of chess, you win by capturing the king. Richard III, the last of 300 years of ruling Plantagents, died on the battlefield, suffering numerous blows.
Henry Tudor, supported by the Lancaster family, became the King of England and married Elizabeth, the surviving princess/daughter of Edward IV and Elizabeth. It achieved the unification of the houses of York and Lancaster.-dp
(resources: http://www.bbc.co.uk/history/people/king_richard_iii, http://en.wikipedia.org/wiki/Richard_III_(play), http://en.wikipedia.org/wiki/Richard_III_of_England, http://en.wikipedia.org/wiki/House_of_Lancaster#Henry_V_and_the_Hundred_Years.27_War_.E2.80.93_the_Lancastrian_war)
