Okay, imagine two people. The first spends nearly all their money on paying for essentials like food and rent. The second is rich and the amount of their income spent on essentials is less than half. When you give each of those people an extra $1000, which will spend the most of that? The one with lower income - the person with more money is more likely to save more (i.e. have a higher MPS) because they can fulfill what they want already.
Does that help explain it?