The earth is heavy and warps the space around it literally, like how a bowling ball on a bed would cause an indentation on the bed mattress. It sinks into the mattress a little, same thing with earth in space (space is the mattress and earth is the bowling ball). The objects circling the source of gravity will be affected depending how close they are to the source of gravity....People on Earth have a lot of gravity but astronauts in space are further away from the source (earth), and are affected less by earth's gravity.

So, time......

You have 2 clocks, one on earth and one in space. The clock on earth is affected more by the gravity so it ticks at a normal speed. The clock in space is less affected by earth's gravity so it ticks slower, this is called time delineation. It affects satellites and astronauts too, they are pre-programmed to account for the time delay. Since time moves slower for astronauts, when they come back to earth their watches will be a few minutes behind the clocks on earth (real time travelers). In theory, if they stayed in space long enough they would return to earth to find they aged very little while everyone on earth got old.

Here is the wiki on time delineation, it probably will explain things a lot better than I did! https://en.m.wikipedia.org/wiki/Time_dilation