A random variable is a function that associates a real number with every result of a random experiment.
We will use capital letters to refer to the above mentioned variables, while the small letters will serve to refer to the concrete values of the above mentioned variables.
Discrete random variables
Discrete random variables are those which can only take integer results.
The result of throwing a dice, the number of the people that comes to an event...
Continuous random variables
Continuous random variables can take any real value within its interval.
The duration of a light bulb, the height or weight of a person, the temperature of a room...