Caesar told Marc Antony, who is running in the Lupercalia celebrations, to touch Calpurnia, Caesar's wife, as he passes by. The Romans believed that women touched or whipped during this celebration would become fertile.
This interaction takes place in Act 1, scene 2. Caesar asks Marc Antony to do this because Caesar wishes to have an heir, who can continue ruling Rome once he dies. This is the audience's first glimpse of Caesar, and it foreshadows the coming assassination of Caesar and the internal chaos that grips Rome in the wake of that assassination as the pro-Caesar and anti-Caesar forces do battle to control the empire.