How to read the Loop's subdivision

I read about the Loop's subdivision but I kept having problem understanding it.

In almost everywhere I searched for info, they wrote that I need to "choose locations for new vertices as weighted average of original vertices in local neighbourhood".



However, I don't understand at all how to choose locations and what weighted average are they referring to. And what are those numbers around the vertices represent and how are they derived?

On a website I found, I see this image:


The algebras around the edges seem to try to tell how those fractions around the vertices are derived. However, I am still not sure what the alpha and "n" variables are referring to.

For a start, what are these alpha and "n" variables referring to? How do I get these values and what do these eventual fractions around the vertices meant for?

Thanks for any help!

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