What are hypergeometric functions in layman terms?

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Could someone please explain what are these in layman terms? Someone here told me that and I still can't figure out what they mean on my own after giving Google a number of hits.

Wikipedia says this: $$ _2F_1(a,b;c;z) = \sum_{n=0}^\infty \frac{(a)_n (b)_n}{(c)_n} \frac{z^n}{n!} $$

What does $(?)_n$ notation mean?

I also fail to see why all this makes any sense. I think I need some layman introduction in very simple terms.