When starlight arrives to your eyes, or to a telescope aperture for that matter, it has transversed tens of kilometers of atmospheric layers. The state of movement, density and temperature it finds in its path varies with altitude, each layer bending rays by a minute amount. This bending effect is known in physics as refraction and has to do with the fact that the speed of light depends on the electric and magnetic properties of the medium through which it propagates. When the beam finds a boundary between mediums of different properties and does so at an angle not perpendicular to it, it changes direction towards the region where its speed is slower.
Since air is not standing still, but is perpetually moving and mixing, the bending effect changes from moment to moment with the end result that what you perceive is the illusion of the light source dancing to and fro. This is the same familiar phenomenon of seeing across the heated air column above a campfire or a hot surface like sun heated asphalt, and you perceive objects beyond the air column simmering. You do not notice this if the observed object has a uniformly colored surface, but it pops up when there is a texture providing visual reference.
Planets, if moderately large, do not twinkle, their disks may not be resolved with naked eyes, but the composite effects of twinkling from different point across their surface tend to average out giving an illusion of steadiness.
When optical aid is applied and you begin to resolve planet or lunar surface details, or deep sky galaxies and nebulae, the twinkling appears again this time in the form of variable blurring. This effect is colloquially known by astronomers as "seeing". Seeing is affected by weather, altitude and seasons, among other factors. Best seeing conditions typically are found in winter under the influence of a cold front and preferably at high altitudes. Most professional observatories are placed in mountaintops seeking the best possible overall combination.
The ultimate vantage point is certainly space, doing away with the atmosphere, and this is why the Hubble Space Telescope was put in orbit over almost 2 decades ago.
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