How does gravity affect a physical clock? In all the explanations for time dilation and how gravity affects time a common example which is used is "Clock near to the ground will tick away faster than clock away from the ground due to gravity".
But what exactly does this mean ? How does a regular clock gets affected by gravity, does the second hand slows down ?
If it has to do something with gravity affecting the inner working of wind up and pendulum clock will this also affect digital clock ?

** I realize I am missing the fundamentals of lotta things in this question, apologies for the stupid question in advance **
If it has to do something with gravity affecting the inner working of wind up and pendulum clock will this also affect digital clock ?


As astrosnapper noted in his comment, gravitational time dilation affects all time-dependent processes. This includes not only clocks (including digital clocks and atomic clocks), but also the rates at which chemical reactions and radioactive decay occur, measured relative to the equivalent process far removed from the Earth's gravitational well.

General relativity is a descriptive theory. It describes what happens, but not why. (Newton's theory of gravitation similarly was a descriptive theory.) What happens is that time flows slowly in the vicinity of a gravitational source compared to how time flows well away from that gravitational source. The time dilation is a function of gravitational potential energy, not gravitational acceleration.

If you want an explanation regarding why this happens, the answer is no one knows. As noted above, general relativity is a descriptive theory. It explains what will happen but it does not explain why.