SPSS nonparametric tests are mostly used when assumptions aren't met for other tests such as ANOVA or t tests.Strictly, most “nonparametric tests” in SPSS are distribution free tests. Oddly, these two concepts are entirely different but often used interchangeably. Second, nonparametric tests are suitable for ordinal variables too. In rare cases they may have more statistical power than standard tests.
Not sure which (nonparametric) test to use? You'll quickly find the answer in Simple Overview Statistical Comparison Tests.