This particular line comes from William Shakespeare´s "Julius Caesar, a historical and tragic play that is believed to have been first presented in 1599. The play relates the historical events that happen during the triumphant return of Julius Caesar to Rome, his display of power, and the desire of several rebellious senators to kill Caesar before he becomes even more powerful than he already is. In this particular Act, Act 1, scene 2, from which the line derives, Cassius is talking to Brutus to convince him to join the rebellion against Julius Caesar, and to help them kill the now almighty man. Brutus still doubts because like others, they almost believe Caesar to be god-like and all powerful; incapable of death, of defeat, or suffering. However Cassius makes his case by telling Brutus of his own witness to the Caesar´s frailties, and very human self. That particular line "And that same eye whose bend doth awe the world" first shows the belief that Caesar is all powerful and undefeatable, is followed and preceded by comments from Cassius that show Brutus that Caesar is human, has frailties, and can be defeated. That is the meaning of the line.
