I am so glad this question was posed! Besides the Tudors, the Wars of the Roses is one of the most fascinating times in English history to me.
I'm not putting these in any particular order:
1) The name "Wars of the Roses" comes from the two rival branches of the royal House of Plantagenet who fought the wars: the house of Lancaster (whose symbol was the Red Rose) and the house of York (whose symbol was the White Rose).
2) Origins of the Wars: The strife between the two families originated when Henry of Bolingbroke deposed his cousin, Richard II. Richard II's government was highly unpopular, thus the nobles championed Henry's succession as King. Richard II was descended from Edward III through his eldest son, the Black Prince. Henry was descended from Edward III's third son, John of Gaunt. Though he claimed the throne, the succession should have followed down the line of Edward III's second son, Lionel, to his grandson Roger Mortimer before it passed to Henry. Richard II was childless and had adopted Roger as his heir. However, Roger was young and the nobles supported the elder Henry over him.Eventually, Roger's claim to the throne passed to his grandson, Richard, Duke of York.
Henry Bolingbroke became Henry IV. His son later became Henry V. When he died, his son (Henry VI) was only an infant. He also, throughout his life, suffered from bouts of madness. His government (mostly run by feuding noblemen) was extremely unpopular. This paved the way for Richard, Duke of York's claims to the throne.
3) The Wars of the Roses can be divided into three parts:
The first is the conflict between Henry VI and Richard, Duke of York (mentioned above). Henry VI's government proved ineffective. In 1455, Richard, Duke of York rose up against Henry VI's government. In 1460 the forces drew a peace treaty in which Richard became Henry VI's heir. However, Henry VI's wife, Margaret of Anjou and her son did not like this compromise. She fled to Wales and gathered support their. During the Battle of Wakefield, Richard was killed. His remaining sons, Edward, George and Richard took up their father's banner.
The second part of the Wars of the Roses was between Richard's son Edward and Henry VI. Like his father, Edward was now considered Henry VI's heir (despite the fact that he had a son by Margaret of Anjou). However, Edward knew Margaret would never allow his succession. He moved toward London with his army. Upon entering the city he was unofficially crowned King by Parliament and the people. He was officially crowned King Edward IV in 1461. Fighting continued and Henry VI was finally captured. He was imprisoned and killed within the Tower of London in 1471. His son and heir was also killed in battle. Edward was temporarily overthrown by his once ally, the Earl of Warwick. However he regained his throne in 1471. For a time, there was peace. Edward IV died in 1483.
The third part of the Wars of the Roses began when Richard, Edward IV's younger brother, claimed the throne over Edward's young son, Edward V. Richard had Edward V and his young brother, Richard, placed in protective custody in the Tower of London. He then had the boys declared illegitimate, thus leaving the throne to himself. Eventually, the two young boys disappeared. They became known as "The Princes in the Tower." Richard III was crowned king in July 1483. Opposition to Richard's rule was quick. Henry VI's claim to the throne had passed to Henry Tudor, a descendant of Edward III through his mother, Margaret Beaufort. Henry Tudor raised an army and invaded England. He defeated Richard III at the Battle of Bosworth in 1485. He was then crowned King of England. He married Edward VI's only surviving child, Elizabeth, thus combining the Houses of York and Lancaster to create the House of Tudor. (Please keep in mind that this is a very general overview of the Wars of the Roses!)
4) Henry VI died after being deposed and imprisoned in the Tower of London. However, his death is still under speculation. Some claim Edward IV had him murdered, but others claim he died of natural causes.
5) Edward IV married Elizabeth Wydville (a minor knight's daughter) in secret. Theirs was a marriage of love, not for political or monetary gain. The marriage was the main cause of the division between Edward and the Earl of Warwick.
6) The Princes in the Tower disappeared in 1483. To this day, historians still speculate whether or not they were murdered by Richard III, Henry VII or possibly the Duke of Buckingham.
7) Men you should know:
Henry VI-King of England
Richard, Duke of York-Claimed the throne, but died in battle
Edward IV-son of Richard, Duke of York. Won crown from Henry VI.
Richard, Earl of Warwick-Known as "the King Maker." Major player in the later battles between Edward and Henry.
Richard III-Brother of Edward IV. Claimed throne after Edward's death.
Henry Tudor (later Henry VII)-Won the Battle of Bosworth against Richard III and founded the Tudor Dynasty.
8) Women you should know:
Margaret of Anjou-Queen of Henry VI
Margaret Beaufort-Mother of Henry VII
Elizabeth Wydville-Wife of Edward IV
9) Battles you should know:
The Battle of First St. Albans-The first battle of the Wars of the Roses. Richard, Duke of York won against Henry VI.
The Battle of Wakefield-Victory for Henry VI and Margaret of Anjou's forces. Richard, Duke of York was killed.
The Battle of Barnet-Richard, Earl of Warwick was defeated (and killed) by Edward IV's forces.
The Battle of Tewkesbury-Victory for Edward IV in which he demolished the Lancastrian forces.
The Battle of Bosworth-Victory for Henry VII against Richard III. Richard III was killed.
10) Despite Henry VII's decisive victory, he and his son Henry VIII were plagued by imposters and claimants until 1525.
These are just a few of the things I think are important. Please feel free to add your own!