What does Cassius mean when he says that "the fault is not in our stars but in ourselves" in Julius Caesar?

Cassius is trying to convince Brutus to kill Caesar by telling him that it is their fault if they let him lead.

At this point, Cassius is the leader of the conspiracy.  When he makes this speech to Brutus, he is telling him to step up, and be a part of it. 

Men at some time are masters of their fates:The fault, dear Brutus, is not in our stars,But in ourselves, that we...

Cassius is trying to convince Brutus to kill Caesar by telling him that it is their fault if they let him lead.

At this point, Cassius is the leader of the conspiracy.  When he makes this speech to Brutus, he is telling him to step up, and be a part of it. 

Men at some time are masters of their fates:
The fault, dear Brutus, is not in our stars,
But in ourselves, that we are underlings. (Act 1, Scene 2)

In a nutshell, this means that people are in charge of their own destiny.  They can succumb to someone else’s rule, or they can make their own choices.  In Cassius’s mind, Caesar is a tyrant.  By just standing back and letting him have his way, they are acting as no better than slaves.

In trying to build Brutus up, Cassius tells him that there is nothing about Caesar that is better than him.  Brutus is the one with noble blood, after all.  Caesar is a self-made man, though he is a Patrician.

Brutus will start a spirit as soon as Caesar.
Now, in the names of all the gods at once,
Upon what meat doth this our Caesar feed,
That he is grown so great? Age, thou art shamed!
Rome, thou hast lost the breed of noble bloods! (Act 1, Scene 2)

The speech seems to work.  Brutus admits to Cassius that he thinks that Caesar is overreaching.  He worries that Caesar is too ambitious.  It does not actually take much to talk Brutus into joining the conspiracy.  Later, when he is by himself, Brutus asks himself why Caesar has to die.  He decides that they need to kill the snake while it is still in its shell.  Caesar has not done anything abusive yet, but it is only a matter of time.

Brutus takes charge of the conspiracy.  He lends it legitimacy with his ancient aristocratic name.  The movement needed him for credibility, but he placed himself as the decision maker.  No longer an underling, Brutus believed that he was doing the right thing for Rome, but he made some bad decisions in the process.