It’s pretty common to fit a function to a dataset when you’re a data scientist. But in many cases, it’s not clear what kind of function might be most appropriate—linear? quadratic? sinusoidal? some combination of these, and perhaps others? Gaussian processes introduce a nonparameteric option where you can fit over all the possible types of functions, using the data points in your datasets as constraints on the results that you get (the idea being that, no matter what the “true” underlying function is, it produced the data points you’re trying to fit). What this means is a very flexible, but depending on your parameters not-too-flexible, way to fit complex datasets.
The math underlying GPs gets complex, and the links below contain some excellent visualizations that help make the underlying concepts clearer. Check them out!