What is the normal probability distribution function?

I've looked at explanations online and they don't make a lot of sense. I understand that "normal" relates to the normal curve, but what is a probability distribution and what is the function actually measuring? Also, please provide an example of using this function in practice. Thank you.

$F(x) = \frac{1}{\sigma \sqrt 2\pi}e^ -\frac{1}{2}(\frac{x - \mu}{\sigma})^2$ 

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