In a Gaussian distribution, what's the meaning of the height (ordinate) at $x$?
according to [1], the funtion is called the probability distribution function of a Gaussian distribution, according to [2], it calculates the height of a Gaussian distribution.
Does this function mean the probability at $[-\infty，x]$, or the height (ordinate)?
TIA.
The function you mentioned (better to write in with MathJax) is NOT the probability distribution, it is the pdf: probability Density function (the ordinate, as you said).
$$ \bbox[5px,border:2px solid black] { f(x|\mu\;\sigma^2)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2\sigma^2}(x-\mu)^2} \qquad } $$
The probability distribution is its integral function
$$\mathbb{P}[X\leq x]=\int_{-\infty}^x f(t)dt$$