what does box mean in this context?

Basically a private area. Especially in theater situations. Balcony situations are often small private areas.

When Lincoln was assassinated, he was in a balcony "box" of the theater. His assassin, John Wilkes Booth a stage actor, was on the theater floor.

Remember this story and you'll never forget what such a box is. You'll likely as well remember the name of his assassin. The word "Booth" was just a coincidence.

It's a theater term for an enclosed, private, seating area. In Regency England, and before, theaters rented out boxes for the season to the families of wealthy patrons. Thus they were ensured of seating at all times.

Sports arenas have the "Sky Box", with a view of the field, and private entry for the families and friends of the team.

They are trying to smuggle things into the theatre inside a box. 🤔

A box is a place to sit. Normally to the side and up so you can see the stage clearer. It's normally reseved for a small group of people

A box is typically a group of seats clubbed together.
Sometimes .. they will have half walls around those groups of seats as an enclosure and sometimes there will be full walls to kind of give you a private space.

You can see the separate box in the rear end of the sitting arrangement.