When Ezekiel Cheever finds the needle stuck into the poppet's belly, he says, 

Why, this go hard with her, Proctor, this—I had my doubts, Proctor, but here's calamity. 

To the courts, the fact that a doll is found in Elizabeth Proctor's house with a needle stuck into its belly when Abigail has seemed to suffer the same affliction, is proof enough of Elizabeth's guilt. This is why he calls it "calamity." Abigail claims that Elizabeth sent her spirit out to push the needle into Abigail's stomach while she sat at dinner. This evidence is called spectral evidence: when, the Puritans believed, a witch would send out her specter, or spirit, to do her bidding while her physical body exists elsewhere. It was decided that the court would accept spectral evidence. This evidence alone was enough to convict some witches because, as Danforth says, no one can see the witch's specter besides the victim and the witch herself. This spectral evidence, the incriminating poppet, and Abigail's testimony regarding each, is plenty of evidence to convict Elizabeth.

In Act II, Cheever comes to the Proctor household to investigate Elizabeth.  He has a warrant to check the house for poppets (homemade dolls).  Elizabeth is confused since she says she "has never kept no poppets, not since I were a girl."

Cheever tells the Proctors that Abigail came to dinner that evening with a needle stuck in her belly.  Abigail has told the court that Elizabeth Proctor sent her spirit out that night and stabbed her.  Cheever and Hale feel that they have the necessary proof, when they see a poppet on the mantel and find a needle hidden inside.

The audience knows that Mary Warren made the poppet and gave it to Elizabeth in scene 2.  Mary Warren tells Hale that she made the poppet and kept the needle inside for safe keeping.  She even points out that Abigail saw he do this, and so should know.

We see here that the courts are not interested solely in the truth.  Even when Mary Warren admits that the poppet is hers, Hale doubts her honesty.

Child, are you certain this be your natural memory? May it be, perhaps, that someone conjures you, even now, to say this?