The way I've understood it is that everything which can 'move' in spacetime has to have a momentum vector with constant magnitude C (when expressed in the right units, C = 1)
The faster you 'move' through space, the more you have to 'borrow' from the time component of the vector to maintain a magnitude of C
That means your 'position in time' moves slower; and so for people who aren't moving as fast through space as you are, they appear to 'experience more time'
The faster you 'move' through space, the more you have to 'borrow' from the time component of the vector to maintain a magnitude of C
That means your 'position in time' moves slower; and so for people who aren't moving as fast through space as you are, they appear to 'experience more time'