When using the "non-informative" prior $\pi(\mu,\sigma)\propto\frac{1}{\sigma^2}$ where $\pi(\mu)\propto1$ and $\pi(\sigma^2)\propto\frac{1}{\sigma^2}$
Where is the no information for the parameter?
and if would be informative prior, Where one would see the 'information' given?
What I've searched
I saw the definition on Wikipedia https://en.wikipedia.org/wiki/Prior_probability and there mentions
An informative prior expresses specific, definite information about a variable. (then an example that I didn't understand).
An uninformative prior or diffuse prior expresses vague or general information about a variable. The term "uninformative prior" is somewhat of a misnomer. Such a prior might also be called a not very informative prior, or an objective prior, i.e. one that's not subjectively elicited. Uninformative priors can express "objective" $\color{blue}{\text{information}}$ such as "the variable is positive" or "the variable is less than some limit".
My question is where is this $\color{blue}{\text{information}}$ given in my particular example, for instance?
What I've understand so far is that instead of saying "the variable is positive" or "the variable is less than some limit" in my case would be: the parameter $\theta$ has $x$ distribution, such distribution is given by the statistician.
Is it wrong?
Help please to understand this (If you could please don't introduce concepts of measure or measure sets because I don't have knowledge on this).
Note: Previously I asked this question (Information about parameters using priors distributions) and was marked as duplicate with other 5 links (What is an "uninformative prior"? Can we ever have one with truly no information?, Why would someone use a Bayesian approach with a 'noninformative' improper prior instead of the classical approach?, Why are Jeffreys priors considered noninformative?, What is the point of non-informative priors?, History of uninformative prior theory) I read them all and there was no answer to this...