A bicycle has two wheels, a binomial has two... nomials, and we (humans) are bipedal - we have two feet! Electricity has two states - on (1) and off (0). This means we need a number system that allows us to count using only two digits.
Our decimal number system has ten 'digits', just like our fingers - which we also call digits (similar to 'digital' - no?). Our placeholders can have any of the digits 0 1 2 3 4 5 6 7 8 9. Once over 9, we increase the next placeholder by one and roll the 9 to 0.
Since electricity can either be on (|) or off (O), ether flowing (1) or not flowing (0), we are unable to use the decimal system to represent numbers - we only have two states, not ten!
Other great videos: - Binary Numbers and Base Systems | As Fast as Possible - Binary Tutorial - written samples