If you've ever used "Bayesian optimization" to choose hyperparameters, that was almost definitely a Gaussian process.

The article focused on the case where you have a finite number of test points, which is probably a good idea for an article like this. Still, there is another interpretation of Gaussian processes where they are actual stochastic processes (hence the name), a probability distribution over a set of functions.

I would have found an article that covered that interpretation even more helpful, although I'm not sure an easy-to-follow version could exist.