Richard II was thrust onto the throne at the very early age of ten, when his grandfather, the much-revered King Edward III, died in 1377. Richard's father was also named Edward, and was known as the "Black Prince"; a promising, warlike and beloved heir to the throne, he unfortunately died the year before the "old king" Edward III, leaving his son Richard to inherit the kingdom the following year. Richard was thus left with very large shoes to fill. His ascension at an early age meant that he grew up as a ruler, and, spoiled by power (at least according to Shakespeare), allowed himself to become reliant upon influential advisors. At several points in Richard II, he is compared unfavorably to both his illustrious grandfather and his tragically short-lived father.
Richard's father was the oldest son of King Edward III, and the rigid English laws of succession meant that the oldest son of the king's oldest son must inherit the crown; thus, young Richard became ruler at ten. However, the Black Prince had six younger brothers, several of whom figure importantly in Richard II. One is John of Gaunt, Duke of Lancaster. He is, obviously, the uncle of Richard II; his son, Henry Bolingbroke, who eventually becomes the usurper of the throne, is therefore Richard's cousin and also a grandson of Edward III. A younger brother of the Black Prince is Edmund of Langley, Duke of York. York is hence Gaunt's brother and Richard's uncle, and his son, the Duke of Aumerle, is a cousin to both Richard and Henry Bolingbroke.
A third brother to the Black Prince was Thomas of Woodstock, Duke of Gloucester. He died under mysterious circumstances shortly before the time at which Richard II takes place. This is the crime for which Gloucester's widow asks John of Gaunt to take revenge in Richard II, when she protests that "One vial full of Edward's sacred blood / ...Is crack'd, and all the precious liquor spilt" (I.ii.17-19). King Richard himself, as well as a number of other noblemen both inside and outside of the royal family, were either active or passive participants in Gloucester's death; it seems that it was Richard himself who gave the order for his execution. Although no one dares to openly acknowledge the king's complicity, this death haunts the play and symbolically seems to both justify and foreshadow Richard's downfall.
The intra-familial conflicts in this play lay the groundwork for what will, in later years, escalate into a monumental struggle between the houses of York and Lancaster. This conflict will, famously, come to be called "the War of the Roses" (after the symbols of each house -- one a white rose, one a red). John of Gaunt, the uncle of Richard II, is the Duke of Lancaster; therefore, his son Henry Bolingbroke (King Henry IV) and all his descendents will in later years be known as the Lancastrians, or the House of Lancaster. There will be strife between this line of descent and the descendants of Gaunt's brother Edmund, Duke of York--whose house will be known as the house of York. Shakespeare has already chronicled these struggles in his first history tetralogy, Henry VI, Parts 1-3 and Richard III. The conflict will not be laid to rest until (as Shakespeare documents at the end of Richard III) a son of the house of Lancaster marries a daughter of the house of York, and, as Henry VII, founds the Tudor dynasty--the one which was still reigning in Shakespeare's time, and to which Queen Elizabeth, the ruler at the time this play was written, belonged.