Caesar is worried about Calphurnia because she tells him that she had a dream that people were bathing their hands in his blood and she is concerned.
Caesar’s wife Calphurnia considers herself somewhat of a prophetess. She keeps Caesar up all night having bad dreams about him the night before the Ides of March. Of course, she knows about the Soothsayer's warning about that day. She keeps crying out in her sleep, “Help ho, they murder Caesar!” (Act 2, Scene 2).
She dreamt tonight she saw my statue,
Which, like a fountain with an hundred spouts,
Did run pure blood; and many lusty Romans
Came smiling and did bathe their hands in it. (Act 2, Scene 2)
Calphurnia wants Caesar to stay home, but Caesar is worried about his reputation. He does not want her to worry about him, but he also doesn’t want to look weak. He agrees to stay home, but she wants him to have Antony tell everyone that he is sick, and he refuses. He doesn’t want to send a lie. Then Decius comes and tells him that the dream really means something else.
Your statue spouting blood in many pipes,
In which so many smiling Romans bathed,
Signifies that from you great Rome shall suck
Reviving blood, and that great men shall press
For tinctures, stains, relics, and cognizance. (Act 2, Scene 2)
Decius convinces Caesar that he can’t stay away from the senate because it will look bad. They are planning to award Caesar a crown, he says. They might change their minds if Caesar doesn’t come. He can’t tell everyone to “Break up the Senate till another time, /When Caesar’s wife shall meet with better dreams” (Act 2, Scene 2).
Decius is very convincing and good at thinking on his feet. He has told Brutus and the other conspirators that no matter what, he could get Caesar to the senate building, and the other conspirators show up after he has already convinced him. Caesar is not suspicious at all. In fact, he asks the men to stay close to him, thinking that they are his protectors and not his doom.
Caesar is a superstitious man, but he is more arrogant than he is afraid. He is convinced that he can outlive danger. He also does not believe in fear. He says, famously, "Cowards die many times before their deaths;/The valiant never taste of death but once." (Act 2, Scene 2) His reputation also matters to him. He doesn't want anyone to think that he has fears. His arrogance is the main reason he doesn't think Decius is playing him.
There is another reason why Caesar is concerned about his wife Calpurnia (Calphurnia). It is shown early in the play. At the opening of Act One, Scene Two, Caesar twice calls to his wife by name. This, of course, is to identify her to the audience. He tells her:
Stand you directly in Antonio's way,
When he doth run his course.
Then Caesar summons Marc Antony to his side and tells him:
Forget not, in your speed, Antonio,
To touch Calpurnia, for our elders say,
The barren, touched in this holy chase,
Shake off their sterile curse.
Caesar is obviously concerned that Calpurnia has been unable to conceive a child. This "sterile curse" affects him directly because he would certainly like to have an heir, preferably a son. He is already thinking of becoming king and probably emperor, and he would naturally like to found a dynasty. When he is assassinated, his heir is his nephew Octavius. So apparently Calpurnia was not affected by being touched by Antony in the Lupercal race.
Shakespeare must have been concerned that there was such an imbalance of male and female characters in Julius Caesar. Only Calpurnia and Portia have significant roles among all those men whom the audience would have a good deal of trouble in telling apart, since there are so many of them and they all dress alike in Shakespeare's idea of how ancient Roman men dressed. Shakespeare makes a big issue out of Calpurnia's nightmare in order to give the female impersonator some exposure for the sake of variety and contrast. Shakespeare also makes a big issue out of Calpurnia's barrenness in order to have at least one female character in the opening scenes of the play. Chances are the same youth played both Calpurnia and Portia wearing different gowns and wigs.
Calpurnia would naturally be very concerned about the fact that she cannot give Caesar a child. It could mean divorce! And Caesar is concerned about her concern as well as being concerned about himself.