I am not entirely sure either, what they mean by hologram. The problem is, that holographic principle ( or similar) can mean different things depending on the c

I am not entirely sure either, what they mean by hologram. The problem is, that holographic principle ( or similar) can mean different things depending on the context. But in string theories, it is sometimes the case that lower dimensional theories can encode the same information as the full string theory. Just as illustration, if the endpoints of your strings are stuck on a two dimensional plane, but the strings can vibrate in three dimensions, then you can potentially describe the system as a theory of the endpoints in two dimensions ( and the vibration mode of the string would potentially be encoded as the type of particle), or you can describe how the strings move through three dimensions. As for recommended reading, I liked Brian Green's The Elegant Universe.