Though Richard III is one of Shakespeare's most well-known history plays, the history of Richard III's reign, as well as the depiction of his character plays a very pointed role in the Bard's depiction. Writing in a period when Elizabeth I, the granddaughter of the Earl of Richmond (later Henry VII), ruled England, it was not particularly intelligent for writers to depict political affairs and those in opposition to the current royal line favorably. Such is the case in Richard III.
In the play, Richard III is depicted as physically deformed, which only serves to accentuate what could only be termed his moral depravity and Machiavellian political outlook. Characters' deformities often reflected their inner nature. Richard III, as Shakespeare portrays him, certainly falls into this category. He is depicted as a character who, though he is fifth in line for the throne, will stop at nothing to achieve - not even murdering (or having others murder) the other heirs to the throne. Two of these heirs are the young sons of the Duke of Clarence (Edward and Richard, 13 and 10 respectively). Though it was a matter of debate in Shakespeare's own time, he leaves nothing for the reader to doubt in his depiction of the course of events. Richard clearly orders the deaths of the two children. This depiction certainly elevated the legitimacy of the Tudor line, whose founder, the Earl of Richmond, righteously kills Richard at Bosworth Field in 1485. In doing so, he killed the usurper and has placed himself as the rightful ruler of England (having married the older sister of the two young princes).
While this is the way that Shakespeare portrays the much maligned ruler, the historical record yields some different interpretations of the events. Most importantly, the nature of politics in Richard's time demanded a large degree of ruthless behavior. In many ways, not showing such ambition was a sign of weakness that could result in a very swift demise. In addition, less than two hundred years after Shakespeare's play, writers had already started to set the record straight. First of all, Richard was not a hunchback. By many accounts, he was a reasonably effective ruler (much more just than his literary counterpart depicts him to be). In addition, the Earl of Richmond's character, rather than being the savior of England as he is in the play, actually tended to behave more ruthlessly than even Richard.
The overall importance of Richard's depiction in Richard III is that it shows the impact history cand, and often does have on literary endeavors.