If a black-hole, in our four-dimensional space-time, encloses a volume then it's counterpart in a hypothetical three-dimensional space-time would enclose an area. The Event Horizons of our BH's are actually (non-material) surfaces (which enclose the volume referred to above) but they're both closed and curved though, and can't really be regarded as a sheet, which I believe should be flat and open. In theory, there's space inside a finite volume for an infinite area because the area can be folded or curled up infinitely tightly. However, quantum issues might prevent the folding or curling from being infinitely tight, in which case the area enclosed within a finite volume might just be very big, instead of infinite. In any case, the folding or curling of the area wouldn't be apparent to anything existing within it's three-dimensional space-time.

I don't know if this is exactly what they're referring to with regard to NS-branes but I suspect it'll be something along those lines.