The data for nonparametric tests is recorded as frequencies not scores. Score implies the numerical result on a test whereas frequency implies the number of times a value recurs. Nonparametric tests can be used "with ordinal or nominal data,... require no assumption about population characteristics", and they compare medians, not means. These tests can be employed "when the population variance is not uniform" and also "with skewed distributions." Some examples of nonparametric tests include Chi-square and Wilcoxon.
Here's an example given by a Professor at the Cognitive, Linguistic and Psychological Sciences department at Brown University that should clarify why the data is considered a collection of frequencies and not scores:
On a flight, the professor decided to count how many people chose chicken or ravioli for their in-flight meal. 83 chose chicken; 117 chose ravioli. These would be the cell frequencies on the chi-square test, not scores. So was the ravioli preference due to chance or was the choice statistically significant? To test this, one would compare these cell frequencies to the null hypothesis expected frequencies.
Terminology is all important in science and math but can make things confusing!