When describing what someone is doing now, you would say "He is reading a book". As a sentence by itself, "He reads a book" is much less usual. It could be used in a stylised present-tense narrative, perhaps.
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AnonymousHe is reading a book.~ He is currently engaged in the activity of reading some unidentified book.
AnonymousHe reads a bookThe simple present usually indicates a habit. In this sentence "he" is not necessarily reading a book at the moment you say the sentence.