A psychiatric observation was a medical order from a certified psychiatric professional where someone can be held in a medical facility should that person be deemed a threat to themselves or others.
Counselor Deanna Troi, in working with Starfleet Command under the urging of Reginald Barclay, threatened Ferengi spy Leosa with such a measure, with extended observation, if she had not agreed to cooperate with authorities for her part in the theft of the Barclay hologram, which was then reprogrammed to steal Seven of Nine's nanoprobes. (VOY: "Inside Man")