What does $\sim$ mean in math and statistics? For example in the following picture above, the red sentence means what exactly with this $\sim$ symbol?

 A: In this context, $X\sim\mathcal{N}(\mu,\sigma^2)$ means that $X$ is a normally distributed random variable with mean $\mu$ and variance $\sigma^2$.
This notation is used when $X$ follows some "well-known" distribution. For instance, you might also see $X\sim\exp(\lambda)$, which means that $X$ is exponentially distributed with parameter $\lambda$.
A: I figured it's worth answering the title question more broadly...
As a general rule, the symbol $\sim$ can be read as "behaves like" or "behaves according to".
In Statistics, it is used to indicate that a variable follows a certain distribution. So, for example, $X\sim N(\mu,\sigma^2)$ can be read as "$X$ behaves according to a Normal distribution". This is the usage relevant in the image in question.
It can be used to express approximation of size of a number - $x\sim y$ can be read as "$x$ is of the same order of magnitude as $y$", and thus they behave similarly in a sense. It is often used in physics to say things like $c\sim 10^8 \text{ ms}^{-1}$, which you can see is not particularly "accurate" as an approximation (as you would expect with $\approx$), but gives a sense of the order of magnitude.
It is also often used to indicate that two things are equivalent in some way. For example, if two triangles are similar triangles, you might have $\Delta ABC\sim \Delta DEF$.
