In addition to the "ordinary" redshifts of distant stars caused by
the relativistic Doppler shift due to the fact that they are actually receding
from the observer on Earth, there is a graviational redshift of
the light from near a large mass M when observed
from a position far from the source, even if the source and observer
are at rest relative to one another. This is not too surprising if we recall
that a gravitational field has to be indistinguishable from an accelerated
reference frame, and an accelerated object cannot be at rest for long!
But an easier way to see the result is to remember that a massless particle
like a photon still has an effective mass 
where (if I may borrow a hitherto undemonstrated result from quantum
mechanics) 
for a photon. Here 
is the frequency of the light and 
J-s is Planck's constant. Anyway, if the energy of a photon
far from M is 
(at 
) then
its effective mass there is 
and as the photon "falls" toward M it should pick up kinetic
energy until at a finite distance r its energy is 
where the new effective mass is 
.
Thus 
and
if we collect the terms proportional to E we get 
where 
. Dividing
through by 
gives the formula for the gravitational redshift,
(I have fudged in that extra factor of 2 that turns 
into the correct Schwarzschild radius 
).
This derivation is completely bogus, of course, but it does indicate why
there is a gravitational redshift.
Given that any mechanism for generating electromagnetic waves constitutes a "clock" of sorts, the waves emitted by such a device constitute a signal from it telling distant observers about the passage of time at the origin. (Think of each wave crest as a "tick" of the clock.) The very existence of a gravitational redshift therefore implies that time passes slower for the clock that is closer to the mass - a result that was referred to earlier without proof.