Two events are independent when the ocurrence of one of them does not modify the probability of the next one.
In this scenario:
Jack rolls a die and writes down the number, then he rolls the die again and writes down the number.
If the die is balanced, each value will have the same probability of happening. When you pick up the die and roll it, it does not matter what number you rolled before, all values still have the same probability.
For example, if you have a
Which means that the events are independent