In Act 1, Scene 1, Richard engages in wordplay to allude to the tumultuous history of the Wars of the Roses, a recurring motif throughout the play:
Now is the winter of our discontent
Made glorious summer by this sun of York [...]
The phrase "the winter of our discontent" as it's used here alludes to the Wars of the Roses, a time of civil unrest and familial conflict. It's a metaphorical "winter," suggesting a time of death, barrenness, and general unease for the play's protagonist. Richard's brother Edward IV has come to the throne, and Richard is painfully jealous and plans to usurp him. By describing this period in his life as a "winter," Richard frames it as bleak and harsh, a period of struggle and hardship. He's unhappy because everyone else is so happy. Shakespeare, here, uses historical allusion to add depth to Richard's words. His original 16th century audience would have been familiar with the history of the conflict between York and Lancaster. Thus, anchoring Richard's unhappiness in real events establishes useful context.
The reference he makes to "this sun of York" is a pun, alluding to both a "son" of York and the actual sun. The "son" in question is King Edward IV, Richard's oldest brother. Edward was famously tall, blond, and handsome, while Richard is believed to have been of lesser height and dark-haired. This allusion to a radiant sun causing "glorious summer" refers to the brief moment of peace and prosperity England had under the first reign of Edward IV. The summer won't last long, as Richard's soliloquy goes on to suggest.
The Wars of the Roses and associated moments of infighting and betrayal recur frequently throughout the play, establishing a motif of destructive familial conflict. This motif is reinforced by repeated references to these wars, the rival houses, and York and Lancaster's house colors of white and red. The repetition emphasizes the cyclical nature of these kinds of skirmishes, mirroring the actual historical events in England that dragged on for over three decades. The violence and repeated betrayals of the York and Lancaster families are echoed in Richard's emotional behavior toward his brothers, as well as his actual deeds. The fact that this motif recurs in every act of the play at least four or five times highlights the pervasive and destructive nature of civil war. It also reflects the constant instability and treachery that characterize the play's political landscape.