What is a Random Variable?
A random variable is an indeterminate whose value will depend on the outcome of a random process.
For example, if we plan to roll a die, we can define a random variable $X$ as the number that will appear. Before the die is rolled, $X$ does not yet have a fixed value, but we can still talk about probabilities such as $\mathbb{P}(X = 3)$, which is equal to $\frac{1}{6}$.
Performing the experiment turns the random variable into a number. But it is very important not to get random variables and numbers confused.
Random variables are fundamental in probability and statistics, which deal with uncertainty. They are used throughout econometric modelling.
It is possible to understand them in a more formal way, as functions, but this slide gives the key intuition.