Parameters in a non-parametric model I have not understood this Wikipedia statement:

The difference between parametric model and non-parametric model is that the former has a fixed number of parameters, while the latter grows the number of parameters with the amount of training data.

How does the number of parameters in a non-parametric model increase with the amount of training data?
 A: Nonparametric methods don't specify something (maybe the distribution, maybe a relationship between two variables*) with a fixed finite number of parameters; they're (potentially) infinite parametric.
Consider a loess curve (a form of nonparametric regression), for example; the parameters not only aren't explicit, if you attempt to count them, the number isn't even an integer.
On the other hand, you never need more than $n$ parameters to define $n$ observations; presumably in at least that sense* the number of parameters grows as you increase $n$.
Consider, for example, a kernel density estimate using the usual AIMSE-optimal bandwidth selection; that has an effective number of parameters (e.g. as measured by Ye's generalized degrees of freedom) that grows as $n$ increases (but not in proportion to $n$).
However, since the statement is referenced (Murphy, Kevin (2012). Machine Learning: A Probabilistic Perspective. MIT), you should probably consult that work for the complete context.
* the second can also be regarded as not specifying something about the distribution, such as the functional form of a conditional mean
**(though in other senses as well)
