To be named emporer during the time of Caesar was often considered equivalent with godhood. In other words, rulers were often considered or considered themselves to be gods. Caesar was no exception to this rule.
In act 2 scene 2 Cassius relates several stories to Brutus in order to point out the weaknesses of Caesar. He tells how Caesar is a weaker swimmer than he; he tells how Caesar was weak and womanish when he was ill. By showing Caesar's humanity, he could more easily convince Brutus to go along with the conspiracy.
Shakespeare may have been making the same arguments against Caesar's deity in this instance. A real god would not be plagued with a sterile wife. A real god could have a child and heir.
Other examples that Shakespeare gives to show Caesar as less than a god are Caesars's "falling sickness" or epilepsy and his deafness in one ear.
Occurring in the first scene, this apparently insignificant passages establishes important themes and motifs: first of all, that this event is a race is important, for the play ultimately involves competition as well as the ambitio. Second, the Feast of Lupercal honors of the god Pan, the queen of fertility. During this time, infertile females are supposed to be able to procreate, and fertile ones are supposed to be able to bear more. And so, second, this race reveals Caesar’s concern about his wife’s infertility, suggesting that he has dynastic aspirations, which, of course, is just what Anthony later argues. Third, the passage establishes the motif of superstition, fate, and personal agency: how much control do we have over our lives? We see this best developed later in the line “The fault, dear Brutus, is not in our stars / But in ourselves, that we are underlings (1.2 ); in the famous “Beware the Ides of March” warning; and then with Calpurnia’s dream the night before Julius’s assassination. Finally, this passage appears to establish the loyalty of Anthony, in that he says “When Caesar says “do this,” I do whatever he asks.” The irony here, of course, is that we know this is not true, for Anthony plots the death of Caesar.
To "cure" her of her infertility. Caesar says in 1.2.8-11: "Forgot not in your speed, Antonio, To touch Calpunia, for our elders say / The barren, touched in this holy chase / Shake off their sterile curse."