Why Stars Twinkle More Than Planets
The atmosphere bends incoming light constantly, but stars and planets do not present the same kind of target to that turbulence.
A bright star near the horizon may shimmer or appear to change color. A bright planet often looks steadier.
A moving optical path
Layers of air with different temperatures and densities bend light by slightly different amounts. As those layers move, the path of incoming light changes rapidly.
Why stars show it so clearly
To the unaided eye, a distant star behaves almost like a point source. Small atmospheric distortions therefore become noticeable.
A planet presents a small disk. Fluctuations from different parts of that disk tend to average together, so it often appears steadier.
Why the horizon makes it stronger
Near the horizon, light travels through more atmosphere, giving turbulent layers more opportunity to disturb it.