Suppose when you add flexibility to your model by adding higher order terms or more predictor variables that you begin to see the test or validation error (MSE or SSE evaluated on the test or validation set) begin to increase away from the training error. What kind of a problem are your models experiencing?

Is this a irreducible error? One that cannot be corrected. I am confused on what the terms irreducible and reducible mean and how they apply to linear regression.