What is the meaning of "this" in the following sentence?
Something this important required complete privacy.
Is the sentence with "this" a grammatically correct sentence structure?
In your sentence, this is used in an adverbal sense meaning to a particular degree. There are several other ways of expressing the same meaning:
She had never eaten this much before
She had never eaten as much as this before
She had never eaten as much before
She had never eaten so much before
Note that this in the the first example sentence is an adverb, but in the second example sentence it is a pronoun (actually a demonstrative pronoun).
You will find both the pronoun and adverb definitions of this in the Cambridge Dictionary.
Something this important required complete privacy.
means
Anything as important as this thing we are talking about required complete privacy.
which really means
This thing we are talking about required complete privacy because it was so important.