The heavens “blaze forth” before the death of Julius Caesar as bizarre occurrences follow one after another; they are omens of terrible things.
The heavens "blaze forth" in Act I, Scene III, when thunder and lightning signal the beginning of strange happenings. During the storm, Casca tells Cicero of having witnessed bizarre occurrences such as the heavens dropping fire; a hand looks as though it is on fire, but it is not burning; there is a lion walking in the capital; and men are on fire as they walk through the streets.
Then in Act III, Scene 2, Calpurnia perceives ill omens, which she interprets as foretelling danger to Caesar. She has seen a lioness giving birth on the streets and warriors fighting fiercely as blood falls on the Capitol. Also, Capurnia warns Caesar:
The noise of battle filled the air, and horses neighed, and dying men groaned, and ghosts shrieked and squealed in the streets. Oh, Caesar! These things are beyond anything we’ve seen before, and I’m afraid. (2.2.21-26)
But Caesar tells his wife that he will go forth since there is nothing to do to stop the gods.
The heavens literally show their disapproval when they "blaze forth". Due to divine selection, Caesar is much more than a modern-day leader. The gods foreshadow the terror and destruction of Caesar's Rome through disturbing astronomical happenings.
The reference is to Calpurnia's plea with Caesar not to go to the Capitol on the Ides of March. She has heard of the terrible storm the night before, and Calpurnia fears that it is an omen fortelling Caesar's death. You may find the passage in II.ii. A description of the storm is also in I.iii, in the speeches of Casca and Cassius.
Note that not everyone views the storm the same way. Caesar, Casca, Cicero, and Cassius all have their own interpretations of the storm's meaning.