I've been looking at the system requirements for some games I want/have, and I'm confused about the processor part.

For example: Theme Hospital requires at minimum 1.8 GHz.

When I go to System on my laptop, it says I have an AMD E-300 APU with Radeon HD Graphics 1.30 GHz. (Using Win 7 64-bit)

Theme Hospital runs just fine in DOSBOX.

Is there something I'm not understanding? Sorry if this seems silly or anything, but I don't have much of a grasp on this kind of stuff. TT_TT

The Ghz isn't a reliable indicator nowadays. As time went on, the real advances in CPU power came from better architecture, improved thermal envelopes, auto-overclocking, multi-cores, and so forth. While emulation can tax a computer system, it can depend on what program is being emulated.

In your case, Theme Hospital works fine. Mileage may vary when it comes to other DOS games, such as Ultima Underworld.

To give you some data, I can run the witcher 2 everything on very high at very 1680x1050 but when I play blood sometimes it lags, doxbox it's an emulator thus it will take a lot more of resources than the original game.
Another thing like they state before ghz is not everything you need to look in a cpu, to give you a random example, an intel Q6600 running at 3.2ghz is far worst than a I5 760 running at 2.8 ghz