This is Tegmark's short formulation of the "mathematical universe" (paraphrased by detractors as "reality made of math"), and he goes out of his way to stress that he means the "is" literally:"Whereas the customary terminology in physics textbooks is that the external reality is described by mathematics, the MUH [mathematical universe hypothesis] states that it is mathematics (more specifically, a mathematical structure)". Deutsche gives a related physical Church-Turing thesis, roughly "every physical process is realizable on a Turing machine", although he is a bit more cautious.
This rings all sorts of Kantian alarm bells for me. The reason for "described by" in textbooks is that "mathematical structure" is a representation, while "physical world" is not, so one can not literally "be" the other for conceptual reasons. Representation by itself is not a representation of anything, it can only represent something else through a correspondence scheme, just like a book without a 'reader' (possibly inanimate) is only an object combining ink and paper. In the case of correspondence to something physical the scheme itself would normally consist of some physical procedures that relate "forces" to forces, "masses" to masses, "motion" to motion, etc. This is how "such and such is described by mathematics" is usually interpreted.
Tegmark's expansive formulation though seems to leave no room for such an interpretation. It would not help to say that the physical procedures involved are themselves mathematical structures, or realizable on a Turing machine, because what we are trying to understand is exactly what it means for the physical to be so structured, or so realizable. We'd be back to the same question, only now asked for the physical procedures that do the corresponding. It would not help to say that in place of "mathematical structure" it means some physical realization of it either, for the same reason, both set off infinite regress.
So what does it mean? If we put "described" back in, then "physical world is described by an abstract mathematical structure" makes sense, but I think that Tegmark wants more, like "fully described". I do not see how to make sense of anything like that though, how does one "animate" idealities without recourse to physical, or to supernatural? Philosophers of old invoked God's powers (sub specie aeternitatis?), but that would hardly work for Tegmark, and it does not explain.