Centering polynomials helps to reduce the collinearity in a model that has interaction and higher order terms. If you do not use centered polynomials, the parameters on lower–order terms are less meaningful. The benefit of centered polynomials is that they make the test for the main effect independent of the test for the squared term.
If you use the center polynomials option, the parameter estimates for the model are centered and are in the scale of the actual factor setting as opposed to being orthogonally coded. The main effects are NOT centered. All continuous terms involved in cross terms or polynomial terms are centered by the mean and the parameters are labeled as such. Centering gives consistent tests that are location invariant.
[Previously JMP Note 37925]