STN-J is a Japan's branch of Solomon, a global organization meant to hunt harmful witchcraft users. STN stands for "Solomon Toukatsu Nin'idantai" (roughly "Solomon Executive Organization"). And the J stands for Japan naturally. The STN-J is lead by Takuma Zaizen, who also leads the Factory.
The STN-J uses different working methods than the rest of the organisation. Something that Robin wondered about when she first time saw them handling a witch. The STN-J uses special bullets called Orbo, which they use to knock out the witch and neutralise their powers. Also the agents from the STN-J usually wear Orbo necklaces to make them immune for Witches' powers. After the witch is knocked out, the agents call to Factory, who then comes to pick the witch up.