Saw a movie today and there was a guy who said
It's important he reads this.
Its beautiful and confusing to me at the same time. What's the grammar structure behind this sentence? Where I can read more about this so I can use it?
This is the subjunctive mood, as @sbutkovi says. The more "correct" way to use the subjunctive mood would be to say "It's important [that] he read this" - where read is the bare infinitive, not conjugated for the third person singular, as it would be in the indicative mood.
"It's important he reads this" is an example of the subjunctive mood, which can be read about more here:
In general, the subjunctive mood is used to discuss things in a hypothetical or uncertain sense.