A simple example is the light in your room. The switch has only two options, on or off. Another example of a binary system would be Morse code. It also works with only two digits, a dot or a dash. Anything expressed in Morse code is done with these two digits.
Electronic circuits work the same way, they are either on or off.
And every sequence of these two signals has a certain meaning. Every communication that takes place inside your computer uses this binary system. If you're not used to them, binary numbers look pretty strange. Converting binary numbers to decimal numbers is not that difficult if you know the secret.