"Very" this sentence means "same". So you could also say "That same night..." it is not necessary in the sentence, but it is used for emphasis. This is a common grammatical structure, especially in written English.

Max was sent to bed without eating anything. On that same night, a forest grew in his room. The word "very" carries the idea of "a surprising coincidence." Suppose I'm shopping at the supermarket, and thinking that when I get home I need to phone a friend named Ken and talk to him about something. To my surprise, I see Ken in the checkout line. "Ken! You're the very man I've been looking for!" Suppose I'm shopping for walking shoes. I walk into a shoe store and say "I'd like some brown walking shoes, maybe New Balance if you have them." The salesperson pulls a box off the shelf and says "We have that very brand and color." "Galileo died in 1642, and Newton was born in that very year."

'Very' in this sentence means same. You could rephrase it saying "That 'same' night...".

It is really a wonderful book!

That is one of my favorite books!