That grid is a representation of space time fabric. The further down it goes the slower time moves and the greater the gravity. Planets and other objects can circle these dips (all objects create them even a speck of dust, it is just some are bigger than others like planets and stars) we call this circling orbits. On that scale they dip down far because the actual distance is infinite as there is a tiny hole at the bottom. Remember that this is expressed in a 2D environment while the actual effect is in a 3d environment.
What this also shows is that the more closely located to a central mass the slower time is. Thus in theory if two people are on sea level the one with the most mass closest to him will move though time the slowest.
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