For classifiers, the RecalibrationFunction tries to adjust the output probabilities so that among the samples that are given output probability of x% of belonging to class y, close to x% of them actually belong to class y. Take a look at here and here (these links give Python code but the idea of calibration is the same).

Feature preprocessing is a completely different thing that involves preprocessing (altering) the features (i.e., inputs) that you give to your models. For example, if your data contains categorical (nominal) data, for example sex, then it's best to convert it to a number before giving it to your model (e.g., 0 for female 1 for male). If you have continuous data with different ranges and scale, for example property prices and property age, then it's best to standardize them. The Classify and Predict functions of Mathematica do this automatically. Look at FeatureExtraction for more preprocessing/feature extraction options.