"how does R do the things it does so well?"

R is a vector/array-based language which fits the problems of its domain in a natural way. On the other hand, you wouldn't really want to use such a language for anything else then data munching.

The language has it's flaws but those are well described, e.g., in "The R Inferno" (http://www.burns-stat.com/documents/books/the-r-inferno/).