I am citizen of USA. I will be flying from South Korea back to USA. There is an 8 hour stop in Taiwan for a connecting flight. Am I allowed to exit the Taiwan airport on this stop to meet up with some friends for a meal? If so, are there any complications I should expect to encounter, such as immigration and luggage check?
As a US citizen you do not require a visa to enter Taiwan.
I have done exactly what you're planning multiple times (most recently last year) and had no issues passing through immigration in either direction. If the immigration staff ask, just explain to them that you are in transit, and show them your connecting boarding pass.
Presuming you are on a single booking, your bags will be checked all the way through, and you will not need to collect them in Taiwan, even though you are entering the country.
As you're talking about 8 hours, this might be a close call. But Taoyuan airport (which I assume you will transfer at) is one of the few airports worldwide that offer a free city tour when you have a long transfer. As a US citizen you're visa exempt so this tour applies to you. You can find more information, the planning and a FAQ about it here: https://eng.taiwan.net.tw/tour/index.htm