Honestly, most of these explanations are all more or less correct but the easiest way to think of it is to imagine an empty fruit bowl with the Earth at the bottom of the bowl and it is rotating. Now imagine rolling a marble along the interior wall of the bowl. The ring traced by the marble that makes the marble’s speed match the rotation of the Earth at the bottom of the fruit bowl is the synchronized orbit.
In astrodynamics and physics this is a subset of solutions to what’s known as a stability problem. You are basically finding out what the minimum required energy is for a system to remain stable.
Edit: When things rotate there is motion associated with the perspective of the rotation. This effect is what’s more or less responsible for the stability.
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