A special care center was a place where individuals who required psychiatric rehabilitation were cared for.
In 2374, after Benjamin Sisko apprised a Federation magistrate of the extenuating circumstances surrounding Molly O'Brien's assault on a Tarkalean, she recommended Molly be taken to a special care center on Dalvos Prime to be evaluated. According to Doctor Julian Bashir, it was the best facility of its kind. Neither Miles O'Brien nor Keiko O'Brien felt the move, which they feared would be permanent, was the best thing for Molly. They felt she stood a better chance of recovering with their help, not that of a therapist who did not know her.
Later, while temporarily being kept in a holding cell, an agitated Molly paced back and forth, making attempts to escape that were thwarted by the cell's force field. Bashir felt that sedatives were only a short-term measure and what she needed were open spaces, something Miles knew a care center wouldn't offer. With this in mind, Miles decided to steal a runabout and return Molly to Golana's past instead, where she was happy. (DS9: "Time's Orphan")