A nonparametric algorithm receives no information from the data scientist about the model it should generate over and beyond the information inherent in the definition of the algorithm itself.
Nonparametric algorithms are suitable in situations where the user does not fully understand the model underlying the available data. The advantage over parametric algorithms is that the user does not have to make assumptions that might be wrong; the disadvantage is that the results obtained tend to be worse because the algorithm has more to learn.