What is a sigmoid function and what does it give as output? I know the equation of the sigmoid function and use it in logistic regression, SVM, etc.
$$
S(x) = \frac{1}{1 + e^{-x}}
$$
In the case of the sigmoid function, What is the exact input and output of this function?
What I know is, it takes the value of x which is written in the above equation. The value of x is the prediction and gives output in a probability value. The probability of a point belongs to a specific class.
Could anyone give me a better explanation of sigmoid function?

If you have a probability $p$ with $0<p<1$ then the odds are $\frac{p}{1-p}$ and the log-odds are $\log\left(\frac{p}{1-p}\right)$.
Your $S(x)$ is the inverse function to this, so $S\left(\log\left(\frac{p}{1-p}\right)\right)=p$ and $\log\left(\frac{S(x)}{1-S(x)}\right)=x$.
It turns log-odds into probabilities.
