What is the significance of the terrible storm on the eve of the Ides of March?

Cassuis believes the great storm is a favorable sign that the conspiracy they have to murder Caesar will be successful. He tells Cicero that the storm signifies the evil they will do.

Cicero converses with Casca, not Cassius during the storm. When Cicero exits the scene, Casca runs into Cassius who characterizes the storm in this way:

There is no stir, or walking in the streets;  

And the complexion of the element  

In favour’s like the work we have in hand,  

Most bloody, fiery, and most terrible.

With these words, Cassius compares the storm to the conspiracy. Further reinforcing the connection, the night of the storm also produces a lion giving birth on the streets, perhaps paralleling the audience's first real look at the conspiracy's being born with the emergence of all its players. Interestingly, the superstitious Romans viewed storms as omens.