Subsites in a webpage (html)

I don't know how this concept is called technically, so I could not search it in the net. My question is as follows:

I have a host, and a domain, let's say : www.host.ex/~myweb, and that is my "homepage". Well, the website have many categories, and I wanted them to be accessed as follows (I have seen this in other websites):

http://ift.tt/2aHsL31

And when I put that address in the browser, it redirects me to that webpage. For my homepage, there is no problem, I have this "public_html" and index.html is there, so when I put www.host.ex/~myweb on my browser, the page is load as expected. However, trying the same approach for these "sub-sites" of my website, the approach does not work. How can this be done? Must I configure something? or put something special in my public_html?

best regards