The full quote is quite long, spanning 21 lines, from line 163-184 in Act II, Scene 1. The jist of it is,
"Our course will seem to bloody, Caius Cassius, to cut the head off and then hack the limbs, like wrath in death and envy afterwards, for Antony is but a limb of Caesar. Let's be sacrificers, but not butchers...Caesar must bleed...Let's kill him boldly, but not wrathfully...Our purpose necessary, and not envious...and for Mark Antony, think not of him, for he can do no more than Caesar's arm when Caesar's head is off".
Brutus has been wrestling with his thoughts for some time, and, in this scene, he comes to the conclusion that Caesar must be killed for the damage he might do to Rome. Although Caesar is his friend, Brutus fears that he is a threat to the well-being of the Republic. While he is ruminating, Brutus is approached by Cassius and others, who would like to overthrow the Caesar. Cassius wants to kill Mark Antony along with Caesar, because he believes Antony is capable of doing much harm himself even after Caesar is gone, but Brutus disagrees. The words quoted above are said by Brutus to Cassius. Brutus, a true idealist, believes that only Caesar should be assassinated; he views Antony as "but a limb of Caesar" who would be powerless once the "head", Caesar, is eliminated. Brutus thinks that if they were to kill both Caesar and Antony, they would be looked upon as "butchers", and he wants to avoid that. Brutus wants the conspirators to be seen as "purgers, not murderers", individuals acting on an ideal, not out of wrath.
This scene is significant because, with these words, Brutus takes over the leadership of the conspiracy, replacing Cassius. As it turns out, Cassius's judgment was sound; Antony does indeed arise on his own to wreak havoc after the death of Caesar.