3Blue1Brown | Fourier series @3blue1brown | Uploaded 10 months ago | Updated 13 minutes ago
A link to the full video is at the bottom of the screen.
Or, for reference: youtu.be/r6sGWTCMz2k

That video tells the story of how this concept was originally invented to solve the heat equation.

Thanks to Dawid Kołodziej for editing together this short