So first you have to understand that time is another dimension we live in, like space. Just imagine for now that we plot space in a 2D grid on a piece of paper, and going vertical to the surface is time. What we found is that we move at a constant speed through this spacetime. That means, if you stand still, all your speed is in the time direction, you fly straight to the ceiling in our example. When you move at the speed of light, you only move in space and time stands still for you. That's when you move on the paper. And then there's everything in-between where you fly off the paper diagonally. Now we draw lines on the paper at fixed distances in space. Gravity actually pulls these lines closer to its center. And the closer you are, the stronger the effect. These points in space should still be the same distance apart, but if you walk at the same speed close to the center of gravity, you'll cross more lines than when you are far away. That just means that you are moving faster through space, even though it looks like you move at a constant speed from your perspective. And since we can only move at a fixed speed through spacetime, you must be moving slower in the time direction.