Meaning

• Any private area, (particularly) bowers in the open air.

• Any private or inner room, (particularly):

• A pew or side-chapel reserved for a monarch or other feudal lord.

• A private cabinet, (particularly):

• Any small room or side-room, (particularly):

• An ordinary similar to a bar but half as broad.

• A sewer.

Meaning

• To shut away for private discussion.

  "The ambassador has been closeted with the prime minister all afternoon. We're all worried what will be announced when they exit."

• To put into a private place for a secret interview or interrogation.

• To shut up in, or as in, a closet for concealment or confinement.

Meaning

• Private.

• Secret, (especially) with reference to gay people who are in the closet; closeted.