The concept of Random Variable is a natural extension of the concept of a random experiment. Let’s recall for that a random experiment is simply a procedure that leads to a non-deterministic outcome (meaning, we cannot predict it beforehand).
For example, a random experiment corresponds to toss a coin. You cannot predict the outcome (can you?), and no matter how much you practice you won’t be able to obtain head or tail at will. Another example, say that you cast a die. If the die is reasonably fair, you won’t be able to predict the number you get every time you cast the die (go and tell those guys in Vegas…)