Please explain the difference between a parametric and a non-parametric test.
Do all data mining techniques come under the non-parametric category?
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A parametric test is a test in which you assume as working hypothesis an underlying distribution for your data, while a non-parametric test is a test done without assuming any particular distribution. Common examples of parametric tests are z-tests and f-tests, and of non-parametric tests are the rank-sum test or the permutation and resampling tests.
Note that in several situations you can choose between one or another. For instance after calculating the Spearman's rank correlation coefficient on a given dataset, you can estimate its significance using either the fact that you can construct a variable $t$ that follows the student's t distribution and estimate its significance from it, or using a simple permutation test to evaluate the null hypothesis.
It is also important to note that parametric tests tend to be more assertive in the sense that they give more specific answers to very well-defined questions.