"Now is the winter of our discontent
Made glorious summer by this sun of York;
And all the clouds that lour'd upon our house
In the deep bosom of the ocean buried...."See in text(Act I - Act I, Scene 1)
Richard uses this metaphor to celebrate his family's present good fortune. Edward, his brother, has just taken the throne from Henry VI. This fortune turns the "discontented winter" into "glorious summer." Richard uses Edward's emblem the sun to metaphorically disperse the clouds over their family's house. Over the rest of the speech, Richard's happiness about the current state of affairs ebbs a bit as he reflects on his deformity —a hunchback—which he claims makes all days winter for him. He reveals his own ambitions for the throne and establishes the desires which will lead to manipulation, treachery, and murder later in the play.
"Was ever woman in this humour woo'd?
Was ever woman in this humour won?
I'll have her; but I will not keep her long..."See in text(Act I - Act I, Scene 2)
The vile King Richard has not only killed Lady Anne’s husband, but he also has successfully wooed her, right in front of her father-in-law, whom he also killed. He gleefully recites this soliloquy, praising himself for wooing Lady Anne’s hand, and foreshadows her death (“but I will not keep her long”). Richard is revealed as a cruel manipulator, using people to further his own ambitions.
"thus I clothe my naked villany..."See in text(Act I - Act I, Scene 3)
Richard boasts of cloaking his evil deeds (his "naked villany") in the "odd old ends" of Biblical verse. Many politicians, both before and after Richard's time, were guilty of masking their crimes with cherry-picked quotes from the Bible. Richard steals "holy writ" in order to "seem a saint when most I play the devil."
"So wise so young, they say, do never live long...."See in text(Act III - Act III, Scene 1)
Richard shows himself to be capable of despicable evil and conniving intentions in this line. He plans to execute children in his ambition to get to the throne. This line is an aside so that the audience understands the full extent of Richard's wickedness, even if the characters on stage are not yet entirely aware.
"Off with his head! ..."See in text(Act III - Act III, Scene 4)
Richard (Gloucester) calls for Hastings to be beheaded, accusing him of "devilish plots" and "damned witchcraft." Hastings thought he was safe in his friendship with Richard, but Richard decides that Hastings must be eliminated because he (like the Queen) is an obstacle in Richard's path to the crown. After Richard tricks Hastings into admitting that anyone guilty of witchcraft (the Queen, allegedly) should be beheaded, he accuses Hastings of witchcraft and orders his immediate execution.
"Dispatch, my lord; the duke would be at dinner:
Make a short shrift; he longs to see your head...."See in text(Act III - Act III, Scene 4)
In this context to make a "short shrift" means to make a brief confession. Ratcliffe asks Hastings to make a short confession before his execution because he is holding up Richard's dinner. With these lines, Hastings realizes that his attempts to seek mercy from Richard and Edward have been in vain; rich men care more for their dinners than for their humanity. Richard's apparently flippant approach to Hasting's execution shows him to be a heartless and ruthless ruler.
"O coward conscience, how dost thou afflict me!..."See in text(Act V - Act V, Scene 3)
King Richard doesn't initially know he has been dreaming. He awakens with frantic demands for a horse and bandages for his wounds, but quickly realizes he was sleeping. He attributes his disturbing dream to his "coward conscience," which has awoken at last.
"tower of strength..."See in text(Act V - Act V, Scene 3)
Though the villainous King Richard III's army has thrice as many men as the Earl of Richmond (later Henry VI), his confidence is shaken in the midst of battle. He (perhaps unconvincingly) assures himself that at least "the king's name is a tower of strength" and is thus capable of wielding power.