Meaning of t (coefficient) in probability generating functions

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Given X non-neg random variable and some $g_{X}(t) = E t^X = \sum_{n=0}^{\infty}t^nP(X=n)$

I am not sure what does "t" represent and how it relates to X?

What are the possible values for "t"? I saw examples of setting t=0, t=1, |t| <= 1 etc, but still not sure about it.

Maybe this is a basic question but a bit lost on how it relates to X.

Could you please explain?

Thanks