Why is Pearson parametric and Spearman non-parametric Apparently Pearson's correlation coefficient is parametric and Spearman's rho  is non-parametric.
I'm having trouble understanding this. As I understand it Pearson is computed as
$$
r_{xy} = \frac{cov(X,Y)}{\sigma_x\sigma_y}
$$
and Spearman is computed in the same way, except we substitute all values with their ranks.
Wikipedia says 

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.

But I do not see any parameters except for the samples themselves.
Some say that parametric tests assume normal distributions and go on to say that Pearson does assume normal distributed data, but I fail to see why Pearson would require that.
So my question is what do parametric and non-parametric mean in the context of statistics? And how do Pearson and Spearman fit in there?
 A: I think the only reason why Pearson's correlation coefficient would be called parametric is because you can use it to estimate the parameters of the multivariate normal distribution. for instance, bivariate normal distribution has 5 parameters: two means, two variances and the correlation coefficient. The latter can be estimated with Pearson correlation coefficient.
Otherwise, you're absolutely right, in order to compute Pearson $\rho$ you don't need to make any distributional assumptions. It's just when you assume normal distribution, the Pearson correlation has additional meanings as opposed to Spearman or Kendall.
A: The problem is that "nonparametric" really has two distinct meanings these days. The definition in Wikipedia applies to things like nonparametric curve fitting, eg via splines or local regression. The other meaning, which is older, is more along the lines of "distribution-free" -- that is, techniques that can be applied regardless of the assumed distribution of the data. The latter is the one that applies to Spearman's rho, since the rank-transformation implies it will give the same result no matter what your original distribution was.
A: Simplest answer I think is that Spearmen's rho test uses ordinal data (numbers that can be ranked but don't tell you anything about the interval between the numbers e.g. 3 flavours of ice cream are ranked 1, 2 and 3 but this only tells you which flavour was preferred not how much by).  Ordinal data cannot be used in parametric tests.
Pearson's r test uses interval or ratio data (numbers that have fixed intervals e.g. seconds, kg, mm).  1mm is not only smaller than 5mm but you know exactly how much by. this type of data can be used in a parametric test.
