"Vengeance is walking in Salem!" means that people are using the witchcraft accusations to get revenge on those who they believe have hurt them, or those against whom they feel jealous, or angry, or just negative in general.
It is important to know how Puritan societies behaved during this time. In general, people were supposed to be worshipping or reading the Bible if they were not working. Any behavior outside of that was considered to be a "vain enjoyment", which was definitely frowned upon. Keep in mind that many people considered it their duty to judge the behaviors of others, and it was considered patriotic and holy to point out the wrongdoings of others, and especially to accuse them of consorting with the devil.
Take that mood of the time, judging others, and add the fact that you can get back at anyone by accusing them of being a witch, and you are using those accusations as vengeance.
"Vengeance is walking in Salem" because one of the long-standing reasons that the citizens are accusing each other of witchcraft is due to grudges they have been holding for decades. In other words, it's not that the accused have actually done what they are accused of doing, but that someone is accusing that individual for his/her own deep-seeded reasons. Since there is such hysteria behind the witch trials, the accusations continue to fly wildly. Vengenace, in that way, has taken human form, and is moving freely through the town of Salem.