Emulation usually requires a lot more processing power than the original platform. The reason is that a good and accurate emulator needs to simulate all the quirks and specialities of the original hardware, but can only do so using software methods. Just one example which applies to the PSP in particular is that it doesn't have an x86 CPU like your PC does. It uses a MIPS CPU with a completely different architecture and instruction set. And all the other components of a PSP (graphic chip, sound chip, memory controller...) are just as exotic from a PC viewpoint.
You often won't get around to create a complete simulation of the original hardware in software.
So when you are playing a PSP game on your PC using an emulator, then your PC isn't running the game. It is running a virtual simulation of the PSP hardware which is running the game.
This additional layer of abstraction requires quite a lot of resources. This is why the first feasible emulators often only appears decades after the release of a system. It just takes that long for a generation of PC hardware to appear which is powerful enough to accurately simulate a past generation of completely different hardware in real-time.
Now that game consoles become more and more PC-like in their hardware design (both XBox One and PS4 use common x86 CPUs and GPUs from AMD which are almost identical to those sold on the PC market), it actually becomes a lot easier to emulate their hardware. But a new obstacle has appeared on the software front. Modern game consoles have very advanced Digital Rights Management systems. They also rely on very sophisticated firmware. Just copying that firmware would be a copyright infringement. Creating a free clone of the firmware would be theoretically possible, but quite a lot of additional work for the emulator developers.