The prediction variance is the variance of observations. It is a combination of the variance of the response (standard deviation squared) and the variance of the predicted mean (standard error squared). The prediction interval represents a specified amount of coverage. The prediction interval is a multiple of the prediction variance.

The prediction profiler does not display the prediction interval. Per the JMP Help:

"The black lines within the plots show how the predicted value changes when you change the current value of an individual X variable. In fitting platforms, the 95% confidence interval for the predicted values is shown by solid blue curves surrounding the prediction trace (for continuous variables) or the height of an error bar (for categorical variables). For continuous variables, the confidence interval region is shaded."

So the shaded area and the interval shown on the left is the confidence interval of the mean response.