Why do stars twinkle but planets appear steady at night?

Stars twinkle because they are so incredibly far away that they appear as point sources of light, essentially infinitely small dots. As their light passes through Earth's atmosphere, small pockets of air with varying temperatures and densities refract the light in slightly different directions moment to moment, causing the brightness and position to fluctuate rapidly, which we see as twinkling. Planets, while still distant, are close enough that they appear as tiny disks rather than true points. Because they subtend a measurable angle, their light arrives along many slightly different paths simultaneously. The atmospheric distortions affecting one part of the disk average out against the others, smoothing the fluctuations and making planets appear comparatively steady to the naked eye.