Any event which might have multiple possibilities implies that the event is variable. For e.g., flipping a fair coin might result into a head or a tail appearing on the coin; this means that the event can take one of the two values, head or tail, hence it is variable. Another example is of rolling a dice which can take either one, two, three, four, five or six; this means that the event can take one of the six possibilities, hence it is variable.
When an event has a chance or probability of occuring then it is called as random. For e.g., there is a ½ = 50% probability of either getting a head or a tail if we flip a coin once. Similarly, there is a 1/6 = 16% probability of getting one of the six values. Hence these events are called as Random Variables because the events can vary & at the same time there is a chance associated with the event occuring.