Let's assume that there are infinitely many humans and that their IQ has a normal distribution with mean 100 and variance 15. Here is a possible experiment:
grab 10 people downtown and measure their IQ
As a mathematical model, we accept the setting that there is a probability space $\Omega$ and "grab human number i" is modelled by a "random variable" $X_i$ which is a measurable function
$$
X_i: \; \Omega \to \mathbb{R}
$$
such that the $X_i$ are independent and have a gaussian aka normal distribution.
When you go out and acutally perfom this experiment, you'll get ten humans and ten values (real numbers) for theiy IQ's. Let's call them $IQ_i$. With regard to our mathematical model, this means that for every human you convinced to do the IQ-Test there is a corresponding $\omega \in \Omega$, each of which is called an event, such that
$$
IQ_i = X_i(\omega)
$$
When you get out again and perform this experiment again, you can accept the same random variables $X_i$ as a model for your experiment, but you'll encounter different humans, get different results from the IQ-Tests, which corresponds to a different $\omega ' \in \Omega$.
Or, to put it shortly as Didier Piau did: The description of the experiment entails as a mathematical model the random variables aka measurable functions $X_i$; but everytime when you actually perform the experiment, it will result in a tuple of values of these functions.