A logic system is one that anything it does can be translated to a true or false, present or absent, high or low, in other words, two opposite and contrasting states where the system can only be at one of them at any one time. Digital electronics use only two voltage levels to work with, one to represent a true, 1 or high (usually 3v or 5v) and another to represent false, 0 or low (a connection to ground, which is at 0v), which make the basis of any logic system.
But what does a true represent in a logic circuit? anything you can think of, it depends on what you are using it to model. One of the most used introductory digital systems is that of a car key alarm, where if the door is open while the key is still in the ignition, a buzzer alarm will sound alerting you not to let the key inside the car when you close it.
To construct a digital circuit for this alarm, you use one input to represent whether the door is open (will be true when it is open, false when closed) and another to represent whether the key is in the ignition (will be true when in the ignition, false when not). For this circuit we want the buzzer to sound when both conditions are true: the door is open and the key is in the ignition.
A digital system is not concerned if the key is only half in, at the on or off position or if the car is only half open or it didn't close correctly; all of these situations are either forced to one state of the other, or switching between both at a very high rate, but it must have one of only two values.
As you can see, we have modeled a fairly complex situation (an alarm controlled by a door and a key) to only two inputs that take only two values. This is what makes digital circuits very useful, they are dependable (a half closed door is an open door, just as a slightly open door).