It works because that is how nature works. Concentrations of mass and energy (in this universe) affect their surroundings by altering time and space.
There is no “explanation” other than observation that time and space is “distorted” by strong gravity and motion. The one concept to get around is that there is no such thing as “universal” or absolute time. What takes 1 second for you might be more or less than 1 second to someone else – there is no “correct” measure of time – it is observer dependent.
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