Can someone explain Time dilation ?

It’s really not that difficult to understand. Relativity tells us that the laws of physics - including the speed of light - don’t depend on how we ‘label’ points in spacetime. We ‘label’ points in spacetime by defining a reference frame where we call our labels spacetime coordinates. So, reference frames can have different spacetime coordinates as long as they preserve the laws of physics and preserve certain invariant properties of spacetime.

One of the most important invariant properties of spacetime is the spacetime interval between two events in spacetime. Even though each reference frame has different choices of coordinates for the events, they have to measure the spacetime separation between the events to be the same. Special relativity tells us how the spacetime coordinates between two inertial reference frames must be related in order to agree on that interval. The math tells us we can describe that as a relative rotation between the two coordinate systems. While the two reference frames agree on total spacetime separation, they cannot agree on how much of the separation is space and how much is time. Einstein’s equations for length contraction and time define those differences.

General relativity is similar, but much more complex. Rather than just relative velocity and acceleration defining the difference in coordinate systems, the coordinate system changes with relative position in the gravitational field. So, measurements of space and time at one point in a gravitational field don’t agree with measures of space and time at other points. These differences are defined by the solutions of Einstein’s famous field equations. Note that all differences are relative. You will NEVER notice any changes in your reference frame.

It's indeed in intriguing question which I also don't understand very well. Why would time progress slower near any massive object? They already proved this on the ISS, even on the top of big towers with atomic clocks they can measure the difference. But the how and why is totally eluding me too. Time is a human concept, I have to admit I am also curious about the possible explanations that are given here, "why does mass slow down time?".

I will give it a try, in just a few words. When you look at something (like a spaceship) moving very fast, the clocks on the spaceship will appear to move very slow. It doesn't matter if the clocks are mechanical, or heartbeats, or someone inside the spaceship playing scales on a piano ... they all appear slow.

Also, it doesn't matter if the spaceship is moving toward or away from you, or going in a circle around you. There is still time dilation. (If the distance is changing, you need to compensate for the time it takes light to get to you.)

Time dilation is very small unless the spaceship speed is very fast. Even at a speed of 10,000 kilometers per second, the effect is only 0.056%.