Omens play a major role within Julius Caesar. Caesar's death is heralded by prophetic dreams and utterances, most notably the dreams of his wife, Calpurnia, as described in act 2, scene 2. Additionally, it is worth pointing out Cassius's dreams of defeat at Philippi and Brutus's encounter with Caesar's ghost. It would be a mistake to underestimate the power of the supernatural in Julius Caesar.
With that in mind, we can consider Casca's misgivings in act 1, scene 3. As he relates to Cicero,
never till tonight, never till now,
Did I go through a tempest dropping fire.
Either there is a civil strife in heaven,
Or else the world, too saucy with the gods,
Incenses them to send destruction.
Consider these last three lines in particular: for Casca, the abnormal weather suggests a world in turmoil, thrown out of its natural order.
Cicero replies to these words by asking whether he's seen anything more extraordinary than this, and here Casca lists a series of strange and extraordinary occurrences, one of which occurred when "the bird of night did sit, / Even at noonday, upon the marketplace, / Howling and shrieking."
For Casca, this is one disturbing omen in a concerning series of them, which suggests to him that the world has fallen into disorder. Meanwhile, there is the conspiracy against Caesar, as well as his murder (which will occur later in the play). That murder seems to be the source of this cosmic disorder and the event which these various omens are pointing toward.