Prior information is the simplest way to implement preference for parameter values or to preferred relationships between them (e.g., a preferred ratio between horizontal and vertical hydraulic conductivity). The sum of squares of departures from these equations contribute to the regularization objective function.
Further reading: PEST Groundwater Data Utilities (5th Ed.), Chapter 2.1.3: The Use of Prior Information in the Parameter Estimation Process.
The general procedure can be explained in comparison to the history matching process: In history matching, the departure of computed observations from their measured values is expressed as a function (measurement objective function). Minimizing this function leads to a parameter set that reproduces the historical measurements, hence a calibrated model is found.
When using prior knowledge, the departure of the applied parameter values from parameter values preferred by the modeller is expressed as a second function (regularization objective function). This kind of regularization is therefore a method that introduces knowledge about the plausibility of parameter values into the calibration process. This knowledge is often subjective, but nevertheless valuable.
PEST implements two principal methods to perform a concurrent optimization on measurement and regularization objective function: Prior Information and Tikhonov Regularization.