Translation:I am reading the book even if you hate it.
The reasoning is simple, 'bok' is a masculine noun, so you'd have to use the masculine/feminine demonstrative, 'den', to refer to it. 'det', however, refers to either an neuter, or something more abstract, which in this case is the act of reading. Another way to phrase that would be "Jeg leser boken selv om du hater at jeg leser (den).", so 'det' would be the replacing 'at jeg leser (den)'.
'jeg leser (den)' has already appeared in the sentence, so 'det' is used to avoid saying it twice.
This is a very good question and I wish I could answer it, since it's the same in my native language (we use the words "selbst = self" and "selbst wenn" = even). But I couldn't find any explanation, other than "selv" referring to oneself being a demonstrative pronoun and "selv om" being an adverb, or a focus particle.
I think "selv" is only used as an adverb in combination with "om", in which case it means "even" or "even if". But I am not sure about that and I would appreciate any input from people who know this better than me. :)