Spoilers if you have not seen latest episode
It is the War of the Roses. The battle between the House of York and the House of Lancaster for who should become king.
Henry VI - House of Lancaster (who was killed with the pillow at the end of the episode) had been king but also suffered from mental health problems. He was married to Margaret of Anjou from France and they had that "strange" son (who was also killed last night in battle).
Because of Henry VIs mental health problems then Edward IV (House of York) was pushed on to the throne (by Warwick the Kingmaker who was also killed in battle last night).
Warwick the Kingmaker then became unhappy that Edward IV had married the "White Queen" - Elizabeth Woodville, so he first tried to get George (Edward's brother) on the throne, then when that failed he "switched sides" (with George) to the House of Lancaster and got Henry VI back on the throne.
Edward IV ran away to Flanders, but then came back with an army and defeated Warwick the Kingmaker (and killed him in battle), then defeated Margaret of Anjou and arrested her, then killed her son Edward in battle, who had been heir to the throne. Then he kills Henry VI with the pillow.
So Edward has now got rid of most of the House of Lancaster "problems" by killing Henry VI, and his son Edward, and arresting Margaret.
George is now back at his brother Edward's side, but Richard (his other brother) and Edward still don't trust him (the "arguing" scene in the Abbey when looking at Warwick the kingmakers dead body).
That now leaves Margaret Beaufort - House of Lancaster (the rather "strange" woman whose husband died in bed at the end of the episode). She is mother to Henry Tudor, who she is convinced is going to be king.
A peek into the future which may help to clear things up, don't read if you don't want to know as it contains spoilers.
Eventually Edward's brother Richard becomes king, called Richard III. But also Margaret Beaufort's son becomes king, called Henry VII. And later they slug it out on the battlefield.
Edward IVs surviving sons, one of whom should have become King Edward V, disappear and they become known as the "Princes in the tower".
Note while it may seem they changed king every 5 minutes, in fact Henry VI was on the throne from 1422-1461 (nearly 40 years, from when he was one year old), then again briefly from 1470 to 1471, when he is killed in the tower of London (at the end of episode).
Edward IV was on the throne from 1461-1470 (9 years) then again from 1471-1483 (12 years).