that is a book.
what is that?
that is a book.
here is a question.may i just say" that is book"?does there have to be “a"? sometimes ,for these countable nouns we don't need to indicate its amount or how many they are ,but rather need to indicate its nature or what it is.therefore i think ,under the circumstances,the word like"a" may be avoided. is my idea right?

Question

that is a book.
what is that?
that is a book.
here is a question.may i just say" that is book"?does there have to be “a"? sometimes ,for these countable nouns we don't need to indicate its amount or how many they are ,but rather need to indicate its nature or what it is.therefore i think ,under the circumstances,the word like"a" may be avoided. is my idea right?

Answer

When a countable noun is singular we must use an article (a/an or the), a possessive adjective (my/ your etc)  or another determiner (this/that) in front of the noun. 'A dog is an animal' (not 'a dog is animal').
There are some nouns that are both uncountable and countable so sometimes they have an article and sometimes not. But the meaning is different. 'That is a glass' (the object). 'That is glass' (the material).

Answer

No, removing "a" sounds like broken English. Bad idea.

Without "a", "book" sounds like the name of a person or a place, or that there is more information to follow (somehow), or that "book" is not a physical thing but an abstract concept. All of which goes against my usual understanding of what "book" means.

With "a", I hear that "book" is a thing, and there is one but I don't know which book; only one possible book out of many.

I'm not sure where you found that idea about countable nouns, but that is the exact opposite to the rule of countable nouns. Just count 'em. :)

Answer

Totally wrong. 
For countable nouns you can NEVER leave out the "a"!