Good day.

I have an older style electrical generator for backup power for my house. It has 2, 20 amp 120 volt, 3 prong plug ins and 1, 20 amp 240 volt , 3 prong plugin( 3 wire). I am installing a manual transfer switch in my house with a plugin located on the outside of the house. The outside plugin is a single 30amp 4 prong setup. Can I connect my 3 wire systen to this 4 wire plugin? I understand that the 4th wire is a neutral wire, What is it for?

I think your question is too technical to trust anybody's answer except tkrussell's. I am only posting to refer you to my thread https://www.askmehelpdesk.com/electrical-lighting/generator-house-123290.html
That may have some other useful information for you.