Put simply, this scene humanises Caesar, who has only appeared up to now (in the play) as a public figure, or in other people's descriptions. We've heard Cassuis pronounce him a "colossus", bestriding the world, we've seen him lead the festivities of Lupercal - and we've heard lots of conversations about him.
Suddenly, in this scene, Caesar is just a man with a wife: and a wife who is worried about him, and who fears for his safety. He isn't immortal, but just another man at the whim of the fates and the gods. Calpurnia - his wife - even gives him instructions:
You shall not stir out of your house today.
What is the point of the scene? It reminds us that, even if Caesar didn't think so, he is just an ordinary man without any supernatural powers. It reminds us that his death is not simply (as Brutus argues) a political move against the "spirit" of Caesar, but the murder of an old man.