The common two-dimensional illustration, in which the weight
of a planet is shown depressing the fabric of a sheet of space, is
misleading. A ball bearing rolling on the sheet and approaching
the planet would be pulled by gravity into the depression,
but—wait—a planet is not pulled down by gravity, and
it attracts an object in space toward its center.
Light takes longer to travel through a gravitational field,
I understand, because increasing gravity is the same as increasing
the density of space. Increasing gravity dilates time and
increases electromagnetic frequencies; decreasing gravity
compresses time and decreases electromagnetic frequencies.
Why this happens, why the shape or density of spacetime
explains what we experience as gravity, to me, is still a mystery,
unless gravitational acceleration occurs simply as a means of
conserving energy and the weights we feel are inertial.
See also in The book of science:
Readings on wikipedia: