What does it mean to say that $G$ has a 'canonical topological generator' $\text{Frob}_{L/K}$?

Question

$G$ is $\text{Gal}(L/K)$ where $L$ is unramified extension (could be infinite) of a local field $K$.

What does it mean to say that $G$ has a 'canonical topological generator' $\text{Frob}_{L/K}$?

Does topological generator mean that the element $\text{Frob}_{L/K} $ generate dense subgroup of $G$? (So Galois group of infinite unramified extension need not be cyclic?)

I know that Galois group of finite unramified extension is cyclic and so there is a way to define Frobenius element using that of the residue fields.

Any help is appreciated. Please explain in what sense the generator is canonical. Feel free to give any reference.