Unlike the "weird" Cell processor of the PS3, the PS4 used x86 architecture (similar to a standard PC). This made it incredibly easy for developers to port games to the system, leading to the massive library of titles we see today.
The PS4's GPU was custom-designed by AMD and was a significant leap in power compared to the PS3. It was capable of 1.84 teraflops, which allowed for much more detailed graphics and larger game worlds.
The PS4's lead system architect was Mark Cerny, a legendary figure who also helped design Sonic the Hedgehog 2 and Crash Bandicoot.