The twinkling of stars (technical term is scintillation) we perceive isn’t due to any intrinsic change in the star’s output*. It’s due to turbulent regions of our own atmosphere distorting the light from the star. This means that effectively light from the star is scattered into or out of our detector/eye and so we see the brightness of the star changing.

There’s some more complex stuff with the light wavefronts being distorted and interference patterns but I’m too rusty on it to remember and explain it, plus the simplified description above is enough (it got me through a Masters thesis on the topic!).

Edit: Also forgot to add, the reason we see stars twinkle while the planets in our solar system don’t. This is because stars are so far away that they’re point sources, whereas the planets are near enough that we can resolve them as disks on the sky with our eyes (it may not look that way but we do see them as more than single point sources with the naked eye). So while the light from the planets (well, reflected by them) is distorted in the same way as described above, it’s effectively being distorted across the extent of the disk from our point of view, so we don’t perceive any change in the brightness.

(*the intrinsic brightness of stars does vary but, on the timescale of twinkling, this variation is way too small to perceive. On longer timescales you can get variations that are large enough in magnitude that you could technically notice it, but again this isn’t what we’d call “twinkling”)