Note: This page is taken from n.wikia.com.
(As written in the N in-game help)
Doors which stay open (and hidden) until you trigger them, at which point they become walls. The triggers are sometimes cleverly concealed, so beware.A trap door appears once the player trips its switch and acts like a locked door. One use of a trap door is to trap the ninja, rendering the level impossible. Oftentimes, the switches are concealed behind objects, usually gold, where one may not see them until it's too late.
There are a few cases where the trap door is actually required to complete the level.