It is complex, and the Radio Times printed a family tree a couple of weeks ago, but even that was hard to follow.
In basic terms it is about two "fighting" families - The House of Lancaster and the House of York. This period was known as the War of the Roses.
Before the series starts Henry VI comes to the throne (House of Lancaster) when he is one year old. But during the next 40 years, as he grows up, he was a bad king (perhaps with mental health problems) and much of the land we owned in France was lost.
So Warwick the Kingmaker (House of York) decided to push Edward IV (also House of York) on to the throne and they defeat Henry VI in battle. Henry VI is captured and put in the tower of London.
But then Edward VI goes off and marries Elizabeth Woodville (the White Queen), much to Warwick the Kingmakers annoyance.
So Warwick the Kingmaker decides to turn his support to George (Edward's brother) to try to make HIM king, and Warwick the kingmaker marries his daughter Isabel to George.
Note that Edward and George also have a third brother, Richard, who stays loyal to Edward, and much later on will become king Richard III.
Warwick the Kingmaker locks up Edward IV and tries to make George king instead, but parliament wont let him and Warwick the Kingmaker and George are in disgrace (the Christmas scene in the second episode) and they have to release Edward IV from prison.
Meanwhile the House of Lancaster are trying to get Henry VI back on the throne.
The rather "strange" woman (who keeps praying) is Margaret Beaufort (House of Lancaster) and her son was from her first marriage to Edmund Tudor (who died in the plague).
Margaret Beaufort is not allowed to look after her son, so he is looked after by Jasper Tudor (who she has been in love with but her mother would not let her marry him).
The few times Margaret sees her son she keeps telling him one day he will be king, which in those days was treason (because he was House of Lancaster). And in fact he will become Henry VII in the future, and end the wars of the roses.
At the end of episode two yesterday Warwick the Kingmaker and George (House of York) decide to "side" with the House of Lancaster to kill Edward IV (also House of York) and put Henry VI (House of Lancaster) back on the throne. They join in this plot with Jasper Tudor (House of Lancaster).
They hope if Henry VI (House of Lancaster) becomes king he will not last long so that eventually George (House of York) will get on the throne.
But their plot is found out (the young boy who runs across to warn Edward IV but is killed by him is from the House of Lancaster and is Margaret Beaufort's brother). Edward IV sees him as a traitor for plotting against him.
So Warwick the Kingmaker, George and Jasper Tudor all need to run for their lives so sail across to Calais. Warwick the Kingmaker takes Isabel, his daughter (married to George and heavily pregnant) but she loses the baby on the voyage.
A son for George and Isabel would have strengthened George's claim to the throne as Edward IV and Elizabeth have only had daughters (hence Elizabeth's comment at the end about expecting a boy).
So we end episode two with Edward IV back on the throne, his wife Elizabeth pregnant (with a boy?), Henry VI still in prison, Warwick the kingmaker and George running for their lives and trying to land in Calais, Jasper Tudor also running for his life, and Margaret Beaufort and her second husband now responsible for looking after her son as Jasper has had to flee.
Pretty simple really !