In order to graphically and orderly present each possible output from a logic gate or any digital circuit, a truth table is used. These tables present every possible combination of input states and its corresponding output.
The first columns represent each of the input variables, and the last one (or few if there's more than one) represent the output of the circuit. For low number of variables (lower than 4 or 5) the number of possible combinations is small enough to be able to represent in a truth table, and all possible input combinations and their corresponding output can be quickly visualized.