A reorientation center was a location where Federation citizens who had committed crimes were placed.

In 2267, Captain Kirk lamented the possibility of putting Khan and his people in a reorientation center after their actions to take over the USS Enterprise, before ultimately choosing to maroon them on the planet Ceti Alpha V instead. (TOS: "Space Seed")

The meaning of "reorientation" is not revealed in the episode, aside from it seeming to be used synonymously with time in prison.