If I'm understanding them right, it's more like this: Imagine flipping a coin and recording the result an infinite number of times. Then your record will include any finite sequence of flips, because any event with a nonzero probability no matter how unlikely will happen if given infinite opportunities. For example you'll get a sequence where Shakespeare's Romeo and Juliet is written in binary with heads as 1 and tails as 0 and vice versa. By an easy corollary of this, any finite sequence of flips will be repeated an infinite number of times. What this person is saying is that they believe the universe is like this; if you decide the location and energy of every electon, neutron and proton in a section of the universe with the same mass as the solar system there's a nonzero chance it'll contain an exact replica of the Earth and everything on it, hence in an infinite homogeneous universe there will be an infinite number of such replicas. Now I don't think this makes sense, because the chance of getting such a replica probably is zero (in the same way that the probability of choosing a random real number and getting 7 is zero), but this is the logic I think.