These exhalations refer to meteors flashing past in the sky. These meteors have a special significance in relation to the political turmoil in Rome. Very soon Caesar is to be assassinated, and in those times it was believed that the deaths of great leaders were foretold by strange warning signs in the heavens.
Calpurnia later makes mention of this belief, on the very morning of the assassination when she reveals her dream which makes her fear for Caesar’s life.
When beggars die, there are no comments seen;
The heavens themselves blaze forth the death of princes.(II.2.30-31)
The meteors appear at precisely the time when Brutus read the forged letters left by Cassius, which persuade him that the people of Rome actively want him to join the conspiracy against Caesar. It is at this moment that he makes the final, irrevocable decision to murder Caesar.
Portentous signs accompany dramatic events throughout the play, such as the great storm which rages when the conspiracy against Caesar begins to take proper shape, and the reported appearance of ghosts and strange beasts in the streets, and so on. All these serve to emphasise the disturbed state of affairs in Rome, and particularly to highlight the unnatural murder of a man by a close personal friend.