The girls were quick to realize the power they had. At first Abigail denies everything and then blames everything on Tituba. Tituba at first denies everything too. When she realizes her life is threatened, she gives her questioners exactly what they want - names. Mrs Putnam starts asking Tituba if she'd seen specific people with the devil and Tituba says yes. From there the hysteria snowballs. The girls start shouting out names of women in the village. As a result, Tituba's life was spared. Abigail suddenly had a lot of power in the village and the bitter, vindictive characters like the Putnams had a way to start knocking off people they didn't like.
Abigail had a lot of power over the other girls. It's shown throughout the play that Mary Warren really feared Abigail. Abigail threatens "a pointy reckoning" for any of the girls who tell. Proctor finally convinces Mary to tell the truth, but Abigail & the girls turn on her in the "yellow bird" scene. Mary is so fearful that she turns on Proctor and goes back to Abigail.
The fear that the other girls had of Abigail, of getting in trouble, etc. kept them going along with Abigail until I think they really believed it. So this hysteria and panic didn't just happen among the townspeople, it seemed to happen to many of the girls themselves. Mary is a prime example of this. This was a big part of what led to the panic.
Hysteria and mob mentality are the main reasons for the panic. Once the notion of witchcraft circulated, one by one the girls either "fell ill" from the effects , or had gruesome tales of attacks by "witches". The hysteria was increased by allowing spectral evidence, which allowed far-fetched accounts of bewitching to be believed. As the hysteria grew, mob mentality became quite evident. They wanted to point to the guilty, have them judged, and executed. If they could name the evil, they did not have to be fearful.