Parametric regression follows an assumption that the data that you use arrives from a distribution. Most commonly used distribution is normal distribution.

While under non parametric regression, usually, there is no assumption that data is from a specific distribution. It can contain data from multiple distributions. Most real world data usually is non parametric when collected continuously. If you are performing an experiment with samples, you might see data is parametric and mostly normally distributed.

@Nagddev is correct. I add following links to relevant articles on the issue of parametric and non-parametric.

LINKS:

http://mlss.tuebingen.mpg.de/2015/slides/ghahramani/gp-neural-nets15.pdf

https://orfe.princeton.edu/~jqfan/papers/01/ant.pdf

Article Non-parametric regression for hypothesis testing in hospital...

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.182.6971&rep=rep1&type=pdf

http://www.stat.cmu.edu/~larry/=sml/nonpar.pdf