Inverse prediction is the opposite of prediction. It is the prediction of x values from given y values. But in logistic regression, instead of a y value, you have the probability attributed to one of the Y levels. This feature works only for two-level nominal responses.
The Fit Model platform also has an option that gives an inverse prediction with confidence limits. See Inverse Prediction in Fitting Linear Models for more information about inverse prediction.
Note: See also Example of Inverse Prediction Using the Crosshair Tool and Example of Inverse Prediction Using the Inverse Prediction Option.