Gray Code input is where only one bit of the input changes at any one time. Incrementing input is where one or more inputs can change at the same time. The advantage of Gray Code input is that, at the moment of change, there is no uncertainty in the output except for the one bit resolution.

An example might be an optical encoder which shows the position of a shaft. Gray Code is much better than Incrementing in this application. Although, modern designs use only two bits in an overlapping style using XOR gates and a flip flop to drive an up-down counter.