Atmosphere is made up of several layers. The layer at the top is optically rare, while the layer at the bottom is optically denser. Due to this, when light travels through different layers of the atmosphere, refraction takes place. since light passes through denser and denser layer as it moves through atmosphere, it tends to bend towards the normal.
Stars are very far from us; compared to planet. Due to this, stars serve as point source of light. As a result, even a slightest change in their apparent position in the sky is clearly perceived by us. Hence, stars appear to twinkle.
Planets on the other hand, are near to us. Hence, they do not serve as point source of light.
Hence, minor changes in their apparent position are not perceived by us. Hence, planets do not appear to twinkle.