The idea is to determine whether Paul has a mind stronger than that of an animal, as “an animal caught in a trap will gnaw off its own leg to escape.”
When Paul sticks his hand in that box, what he feels is an ever-increasing heat that makes him feel like his limb is being burned off.
If he tries to pull his hand out, Reverend Mother Mohiam will prick him in the neck with that needle, which sports a poison that will kill him.
Not only will it be a key moment early in Dune that will have the protagonist demonstrate his mettle, but it should also be a solid acting moment for Timothee Chalamet as he has to sell the audience on him being it truly wretched pain.