We're decomposing a time series here with the STL algorithm. There are other methods of decomposing time series—you may be familiar with one: the discrete Fourier transform. If your data is a time-based signal (like electrical pulses or music), a Fourier transform essentially allows you to decompose a time series into various parts. Bear in mind that they are no longer seasonality and trend, but rather decompositions of different time and frequency domains.

This begs the question: what is the point of decomposing a time series?

A primary reason why we do any machine learning at all is to be able to predict values based on an input. When done on time series, this is called forecasting.

Think about this for a bit: if a time series is made up of multiple components, wouldn't it be better to be able to predict per component? If we are able to break a time series up into its components, be it by STL or by Fourier transforms, we would get better results if we predict per component and then recombine the data at the end.

Since we work on STL, we already have our series decomposed. A very simple exponential smoothing algorithm invented by Holt in 1957 allows us to use the trend and seasonal components, along with the original data, to forecast.