What does "here is all the invisible world, caught, defined and calculated" symbolize in The Crucible?
The first answer is right to say that the town is under siege, but I do not think that is really captured in the quote you cite. To me, this quote is about the ways that people use the invisible world for their own ends.
The quote you cite talks about the invisible world being "caught, defined and calculated." Who has caught it, how have they defined it and what are they calculating?
The people who have caught it are those who have power or want power. They are not accusing and punishing people because they think they are guilty. They are doing it because it can help them get what they want. Parris wants to use the invisible world to make himself look more important. Putnam wants to use it to destroy his enemies. Danforth also wants to use it to keep his authority strong. Abigail wants to use it to get revenge.
In this play, the real people are using the invisible world -- they are defining it and calculating how it can help them. So the quote symbolizes or refers to how the hysteria is driven by the ambitions of various people.
In the play The Crucible the town is under siege from paranoia based on the thought that the devil is at work among the people. The girls in the town led by Abigail have made accusations of witchery and devil crafts among the people. As a result many people have been arrested and kept under lock and key awaiting their trails and convicted of crimes of which they were innocent.
The statement is relative to the town being controlled by the actions of the men who think that the people are guilty. Even when Reverend Hale has found them innocent Danforth wants to have them hung. The invisible world is the containment and the raw belief in what Abigail and her friends have stated. The girl's calculated accusations have led to incarcerations and later deaths of people.