The significance of this passage is that the whole conspiracy plot, and Caesar's life, depends on his decision to go, or to not go, to the capitol. The conspiracy wouldn't have taken place, and Caesar wouldn't have died, if he had obeyed Calpurnia and stayed at home.
This takes place in Act 2 Scene 2, lines 65-107. And is written as follows.
CAESAR: Shall Caesar send a lie?
Have I in conquest stretch'd mind arm so far,
To be afeard to tell greybeards the truth?
Decius, go tell them Caesar will not come.
DECIUS: Most mighty Caesar, let me know some cause,
Lest I be laugh'd at when I tell them so.
CAESAR: The cause is at my will: I will not come;
That is enough to satisfy the Senate.
But for your private satisfation,
Because I love you, I will let you know:
Calpurnia here, my wife, stays me at home.
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.
And these does she apply for warnings and portents
And evils imminent; and on her knee
Hath begg'd that I will stay at home today.
DECIUS: This dream is all amiss interpreted;
It was a vision fair and fortunate:
Your statue sputing blood in many pipes,
In which so many smiling Romans bath'd,
Signifies that from your great Rome shall suck
Reviving blood, and that great men shall press
For tintures, stains, relics, and cognizance.
This by Calpurnia's dream is signified.
CAESAR: And this way have you well expounded it.
DECIUS: I have, when you have heard what I can say:
And know it now. The Senate have concluded
To give this day a crown to mighty Caesar.
If you shall send them word you will not come,
Their minds may change. Besides, it were a mock
Apt to be render'd, for some one to say,
'Break up the Senate till another time,
When Caesar's wife shall meet with better dreams.'
If Caesar hide himself, shall they not whisper,
'Lo, Caesar is afraid'?
Pardon em, Caesar; for my dear dear love
To your proceeding bids me tell you this,
And reason to my love is liable.
Caesar: How foolish do your fears seem now, Calpurnia!
I am ashamed I did yield to them.
Have I in conquest stretch'd mind arm so far,
To be afeard to tell greybeards the truth?
Decius, go tell them Caesar will not come.
DECIUS: Most mighty Caesar, let me know some cause,
Lest I be laugh'd at when I tell them so.
CAESAR: The cause is at my will: I will not come;
That is enough to satisfy the Senate.
But for your private satisfation,
Because I love you, I will let you know:
Calpurnia here, my wife, stays me at home.
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.
And these does she apply for warnings and portents
And evils imminent; and on her knee
Hath begg'd that I will stay at home today.
DECIUS: This dream is all amiss interpreted;
It was a vision fair and fortunate:
Your statue sputing blood in many pipes,
In which so many smiling Romans bath'd,
Signifies that from your great Rome shall suck
Reviving blood, and that great men shall press
For tintures, stains, relics, and cognizance.
This by Calpurnia's dream is signified.
CAESAR: And this way have you well expounded it.
DECIUS: I have, when you have heard what I can say:
And know it now. The Senate have concluded
To give this day a crown to mighty Caesar.
If you shall send them word you will not come,
Their minds may change. Besides, it were a mock
Apt to be render'd, for some one to say,
'Break up the Senate till another time,
When Caesar's wife shall meet with better dreams.'
If Caesar hide himself, shall they not whisper,
'Lo, Caesar is afraid'?
Pardon em, Caesar; for my dear dear love
To your proceeding bids me tell you this,
And reason to my love is liable.
Caesar: How foolish do your fears seem now, Calpurnia!
I am ashamed I did yield to them.
Give me my robe, for I will go.
