Do you know what happened in the movie 'Interstellar',
when the protagonist returned from his voyage
and found that his daughter was even older
than him?
Well, I'll tell you how that happened.
You all must be familiar with the name of
the famous scientist Albert Einstein, he was
the one who suggested that space and time
are interrelated where space is the three-dimensional
world we live in.
Both of them are together termed as four-dimensional
spacetime.
Every object in the spacetime curves it.
The heavier the object, the greater is the
curve.
This is what we call warping of spacetime.
Let's take the example of putting a ball on
a bedsheet.
When we stretch the bedsheet and put a ball
on it, we'll observe that it creates a curve
at that place and the heavier the ball, the
larger is the curve.
The warping of spacetime is the reason that
the earth revolves around the sun because
mass of the earth is comparatively very small
than that of the sun, so the sun creates a
huge warp in the spacetime causing the Earth
to eventually revolve around it. Now the
question is why doesn't the Earth bump into
the Sun?
The answer is as simple as that.
It's because the Earth has also deformed the
spacetime a little bit and hence maintains
its balance.
This states that a massive object warps the
spacetime more so its gravity will be larger
or in other words, greater the gravity, greater
will be the warping of spacetime.
In the same way, a black hole is much more
massive than the stars  and it has
a very high gravity
that even light can't escape from there.
thus, it creates a huge warp in the spacetime
continuum.
Let me explain you with the help of an example.
Suppose we have to move in spacetime from
point A to point B and from point C to point
D, where points A and B are in less warped
region and points C and D are in the more
warped region.
We all know the simple equation that speed=distance/time,
where the speed of light is always the same
approximately equal to 300 million m/s, which
means that time is directly proportional to
distance when speed is constant.
So this indicates that in a more warped region
of spacetime i.e. in the area of strong gravity
the distance of traveling increases and thus
time being directly proportional to distance,
increases.
Hence, showing that in the region of a strong
gravity, time slows down.
This is what is called Gravitational Time
Dilation.
And this is what happened in the movie 'Interstellar',
the protagonist went to a planet which was
very near to a black hole where time slowed
down for him but not for the people who were
on Earth because they were in a weak gravity
as compared to that of Black Hole.
That's why when he returned, his daughter
was older than him.
So now I don't think you have any confusion
about what Gravitational Time Dilation is.
And Gravitational Time Dilation is also the
reason why the Earth's core is approximately
2.5 years younger than its surface because
Earth's gravity decreases as you move away
from the center of Earth and yeah this is
also the reason your head is slightly older
than your feet.
