What" is usually a question word.
Examples:
"What are you doing?"
"What are these?"
"What is your idea?"
"What" can also be used with the meaning of "the thing or things".
Here are some examples:
"What you need is a good night sleep." (= The thing you need is a good night sleep.)
"We don't know what to do." (= We don't know which things to do.)
"You know what to do." (= You know which things to do.)
"That" is used to describe and define the thing you are talking about.
For example:
"I want the pen."
"Which pen?"
"I want the pen that is on the desk."
Here's another example:
"I saw that girl."
"Which girl?"
"The girl that you invited to the party."
Now, regarding your specific sentence:
"The book what I need" would mean "the book which thing I need."
This doesn't make sense, does it?
On the other hand: "The book that I need" makes perfect sense, because you are giving a description of the book. - See more at: http://www.helping-you-learn-english.com/difference-between-what-and-that.html#sthash.GSOg7JPb.dpuf