Considered by many to be "the father of the modern classical guitar," it would be hard to overestimate how dramatically he transformed the landscape and shaped the future of classical guitar as we know it. Take John Williams -- No, not THAT John Williams! -- and Christopher Parkening, for example. While I'm more familiar with them than I am with Segovia, both were profoundly influenced (and even taught) by the giant, Andrés. Without him, they probably would not be.
But the impact of his performing and teaching is a fairly abstract consideration, really. Just try listening to him for a bit, because that's where his true genius lies. (And besides, that's the real reason for his impact, right?)
So here's some Bach (transcribed by Segovia himself.)