Computers store data in little switches, with 2 positions, on and off. To turn these into numbers, they think of each of them as 1 for on, and 0 for off. Try playing with a light by clicking on it.
Since each of these switches has 2 positions, each switch doubles the number of combinations. To keep track of them, we think of them in base 2. With 3 buttons, we have 8 combinations, from 0 to 7, try to get to 7!.
We normally think in decimal, or Base 10, meaning every place is 10 times as much as the one on the right, going from 1 to 10 to 100. In Binary, or Base 2, each place is worth twice as much as the one on the right, going from 1 to 2, to 4. Try making a 10 with the lights!