So what is your question? You just answered it yourself in your post :) /home/index maps to HomeController and the action Index.
routing in episerver is a bit more trickier compared to vanilla mvc. for instance, you might have "/this/is/a/page" map to HomeController that is located directly under /Controllers directory. EPiServer tries to understand incoming request, find matching page (actually content) and tries to invoke corresponding handler (controller in this case) for that request.
There was actually a blog post published recently about routing in Episerver http://bergdaniel.se/join-me-on-a-journey-through-the-asp-net-pipeline-in-search-of-episerver-part-one
I am new to epi server cms. I am using asp.net mvc. currently learning from http://world.episerver.com/documentation/cms/get-started-with-cms/4--adding-website-functionality/
however, I would like to know which controller,view a url is pointing to.
http://localhost:1234/Home/Index // this tell me home= controller and Index = action.
below routing tables I understand.