Basically a media server appliance, the first (white) Apple TV in 2006 was not very good. PC makers have been pushing media servers for years, as unsuccessfully as they had been pushing tablets. Apple needed to rethink the problem, which the second (black) Apple TV did.
It wasn't a media server, but rather, a new kind of set-top box that draws programming from on-demand services (first iTunes; later Hulu and many TV networks). Plus, unlike competing devices, it acts as a relay point for all sorts of entertainment from users' devices: Macs, PCs, iPhones, iPads, and iPod Touches.
The Apple TV is a content nexus, and that notion fits nicely in the mix of personal and connection that other Apple technologies simultaneously proffer.