What's the role of the detailed descriptions of the other planes of existence? Why it was important for the Buddha to tell them?
Mr Ivan ("god is merciful"), because the Buddha did not like Mr Ivan to mistake an realm of existence for Nibbana, or the heartwood. That is why he described those states of being in detail. So when you start to travel, and do not just ponder why you should not travel yet, Mr Ivan is well prepared.

In which plane of existence did you now take place? Nobody aside of Mr Ivan would know that, does Mr. Ivan do?

(Note: this answer has not been given with the agreement to be means of trade or the purpose of/for trade and/or keep people trapped and bound. How you handle it lies in your sphere, but does not excuse the deed here either.)