Shakespeare uses thunder and lightening to not only to complement his theme of fate vs. free will as well as to enhance the mood of the play. Most of the storming occurs while Cassius is convincing Brutus to kill Caesar, and while Brutus is deciding whether or not to help. It is a simple, but effective way, to heighten the frightening and conspiratorial atmosphere.
In addition, the way Shakespeare's characters react to the storming is important. Casca is frightened of it and Cicero says no one should be outside in it--common reactions, especially in a time when people thought storms were the cause of the gods. The only reason the gods would send a storm is if they were angry with something that was happening on earth. Cassius, on the other hand, is defiant of the storm--in fact, he tempts the lightening to strike him if the storm is in reference to him. This is Cassius's first misinterpretation--or unwillingness to interpret--of omens sent to warn him against his actions. He is unable to correctly interpret omens until Act Five.
Act 1, Scene 3, opens with thunder and lightning. By now, the audience is aware of Cassius's malice and has learned of his efforts to persuade Brutus to join his nefarious plot. Many of his co-conspirators have gone around Rome attempting to dissuade citizens from supporting Caesar. They have marred many of his statues and icons, and eagerly encourage others to do likewise.
Dissent and disruption are afoot, and Shakespeare uses the unpleasant weather as an indication of perturbation in Rome. The terribly adverse conditions are portentous of an upheaval. They foreshadow a coming destruction of the natural order. Depicting future mishaps by symbolically using dramatically inclement weather is a favorite dramatic technique employed by Shakespeare. It adds to the drama and tension, and enhances the audience's expectations of the events about to unfold.
Two conspirators, Casca and Cicero, comment about these aspects of the weather, further increasing the audience's hope for gripping entertainment. Casca asks Cicero:
Are not you moved, when all the sway of earth
Shakes like a thing unfirm?
It seems that the earth is also trembling - an indication of something truly terrible coming. Casca remarks further that:
Either there is a civil strife in heaven,
Or else the world, too saucy with the gods,
Incenses them to send destruction.
The gods, it seems, are upset either with each other or with the humans who have been disobedient. It is for this reason, Casca believes, that they are lashing out. He mentions some other strange and unnatural events he has been seeing and concludes that:
When these prodigies
Do so conjointly meet, let not men say
'These are their reasons; they are natural;'
For, I believe, they are portentous things
Unto the climate that they point upon.
At this point, the audience is literally at the edge of their seats and relishing to see what happens next. Shakespeare has masterfully prepared his spectators to expect a feast of intriguing and exciting occurrences, and they will most certainly not be disappointed.