For linear functions, the rate of change is constant, meaning that for each step in the $x$-direction, the change between $y$-values is the same. The rate of change for exponential functions, however, is not constant. Consider the following tables with the same $x$-values.

The difference between the $y$-values in the left table is constant ($+2$), but that's not the case for the right table.

Therefore, the left table represents a linear function, whereas the right table represents a non-linear function. Notice how, for the table on the right, the $y$-values double for each step in the $x$-direction. Thus, every $y$-value is multiplied by $2$ to get to the next.

While the left table corresponds to a function with a constant increase, the right table corresponds to a function with a constant multiplier. This type of function is an exponential function.