The line is Cassius's, spoken to Brutus in Act I, scene 2, and it means that men are sometimes masters of their own fate: if they live as underlings, the responsibility is theirs, not the sky's.
Cassius says this after describing Caesar as a Colossus who dominates the narrow world, while Romans, small men, walk beneath his legs in search of dishonorable graves. The line comes in the middle of Cassius's attempt to persuade Brutus: shortly after, he asks what there is in the name Caesar that is not in the name Brutus.
The play, however, does not stop there. In the stormy night (Act I, scene 3), the same Cassius reads the portents as a warning from heaven against a man who has grown too great, while Cicero reminds us that men interpret events in their own way. In Philippi (Act V, scene 1), Cassius, who followed Epicurus, says he has changed his mind and now gives some credit to omens, after the eagles of the army vanished and ravens began flying over the troops.
The idea of fate appears in other speeches too. In Act II, scene 2, Caesar answers Calpurnia's fear by saying that the end marked by the gods cannot be avoided, and Brutus, after the murder, says "We shall learn your designs, Fate" (Act III, scene 1). What remains is the contrast between Cassius's line in Act I and his confession in Act V.