In the single scene in which she appears, Calpurnia personalises the character of Caesar: for the first time, you realise that Caesar is not just a political name, but an ordinary man with a wife, and a home.
Caesar's own character is also thrown into relief: we see the kindly old man prepared to throw aside his political career (casting aspersions over Cassius' assertion that Caesar is obsessed with the crown) simply to please his wife and assuage her worries about her bad dreams.
You might also want to argue that Calpurnia's "spiritual", instinctive perspective is quite at odds with the cold, power-driven politics of the rest of the play: a "female" perspective which momentarily interferes with the "male" atmosphere?
Inspite of Calpurnia's brief appearance, her role and character are important because:
1. To contrast the private, domestic life of Caesar with his public political life: Caesar makes his first appearance on the stage in a "nightdress" and the very first lines that Caesar utters refer to his wife, "Thrice hath Calpurnia in her sleep cried out/'Help ho! they murder Caesar." From the beginning of the play till now all that we have heard about Caesar relates to his warrior like and statesman like qualities. But, Shakespeare foregrounds his first appearance on the stage by presenting him as a worried and anxious husband who is ready to please her initially by agreeing not to go to the Senate,"and for thy humour I will stay at home."
2.To contrast fate and human will: Calpurnia's intuitive fears,"O Caesar these things are beyond all use/And I do fear them," are contrasted with Caesar's self confidence, "It seems to me most strange that men should fear/Seeing that death a necessary end/Will come when it will come."
3. Calpurnia's interpretation of her dream is brushed aside and Decius' interpretaion is accepted by Caesar to emphasise the significance of the public and the political over the private and the domestic, "How foolish do your fears seem now, Calpurnia."
4. Calpurnia represents the fear and the superstitious beliefs of the contemporary Elizabethan audience concerning the supernatural.