i got many explanation and proving that relative velocity causes time dilation. Einstein's moving light experiment proves it. but that is a clock works with light detector. as detecting the light gets latter the clock works slowly. but in reality how a real watch can be slowed down? And won't the man feel that the time is moving slowly as he knows the general speed of the clock? Sources says that if a man goes to space with very high speed if he returns after few years as his clock moved slowly earth would be moved for many years forward. But my doubt is won't he feels the fact that his clock was slow and he spend many years in space? If he won't feel it how does it happens? and how is he not getting older?
Have you ever draped a measuring tape from point A to point B in a looping indirect path and asked yourself why the path length of the tape is longer than the direct path between A and B?
The answer is that tape measures don't measure distances between points. They measure the length of the path they are on.
Well, it turns out clocks don't measure the time between points. No clock does. Not a light clock. Not a human brain. Not radio carbon dating. Nothing does that. Just like no tape measure measures distance, it only is capable of measuring the length of its own path.
So there is a 4d spacetime. Imagine the z direction as time. Each xyz giving and xy spatial point and z giving the time. Then a particle at rest is a vertical line. And a particle moving in the x direction is a line in the xz plane and a the steeper the line, the slower the particle is going. Each point just spells out a place and time something was located. It gives a when-where.
So clocks make paths in the 4d space. And like a tape measure they are only capable of measuring the length along the curve they actually make. You could have a straight path. Or a curvy one and the measurements will be different.
And nothing does anything other than measure along the path it goes.
You brain, the light clock, a spring clock, a quartz clock, each one changes not based on time, but along the length of their own path. Just like the tape measure makes its marks along its own path.
So now by moving clocks along different paths it is up to us to experimentally find out what lengths look like in the 4d space.
And it's different than you might expect. For instance, the direct path between one when-where and another when-where gives the longest length (not the shortest).
And we also learn in general relativity that passing through a region in a deeper gravity well could make your path shorter. So the longest path from here-now to the other side of the sun six months later isn't to go straight towards the sun at a slower speed, but instead the longest path is to go around the sun like the earth does.
In fact, we found out that is why the earth goes around the sun. When you learn the way the world is, and replace your ideas about what is natural with those ideas then the world actually makes more sense.
Here's a very vague analogy. If we walk at the same speed, but in different directions, say in straight lines, then we would feel as if we are travelling at the same speed but if I measure your distance travelled in my direction, you would have travelled less than I in the same amount of time. If you think of the road as my perspective, then you could say that in my perspective you travelled slower than I. Likewise in your perspective I travelled slower than you. Note that this remains true if you and I were robots that just mindlessly measure each other's travels in our individual perspectives.
In reality time and space are part of the same spacetime continuum, and our paths are not paths in space over time, but paths in spacetime. In a vaguely analogous sense to the above paragraph, each of us feels normal in our own perspective, but observe the other to be travelling differently when viewed from our perspective. This is not merely a mental phenomenon, as the analogy suggests. We literally travel normally, just in a non-parallel direction in the spacetime continuum.
If you think about it carefully, it also explains the twin-paradox because one twin travels in a constant direction in spacetime, whereas the second has to change direction if he ever wants to return to a point with the same space coordinates as the first twin. The twins end up at different time coordinates.
I doubt there is an "intuitive" way to describe time dilation, since most people's intuition suggests against it, but there is probably a way to get the general idea without using a bunch of math.
So, the starting point for understanding the theory is that, as you've probably heard many times before, the speed of light is always constant for all observers. We know this through observations and measurements, and these observations are the ones that go against our intuition, and this presents a problem for pre-relativistic theories.
Trowing a ball inside a moving train
To understand why this is a problem, imagine what happens if you are standing in a moving train, and throw a ball at a certain speed in the forward direction of train's movement? To all observers inside the train, this ball will appear to be travelling at a certain speed $v$ until it hits the front of the train (ignoring forces like friction and gravity for the moment). But, to stationary observers outside the train, looking at the ball through the train's window as the train passes by, ball will appear to be travelling much faster, its speed being accumulated to the speed of the moving train. These two observers, having different (but constant) speeds relative to each other, are said to be in different reference frames.
Turning on a flashlight inside a moving train
Now imagine you wanted to measure the speed of light using a flashlight, inside a moving train. To measure the speed of light, you place two observers on the train, equipped with two synchronized clocks, one at the back of the train and the other one at the front of the train. The back observer fires the light-beam exactly as he passes a certain point on the stationary train station and marks the time on his clock, and the front observer marks the exact time the light-beam hits the front of the train. Diving their distance by the measured time gives them the speed of light, $c$.
At the same time, two carefully placed stationary observers are standing next to the train tracks, again equipped with two synchronized clocks. They place themselves so that the first of them is at the mentioned point on the train station (to record the moment the light-beam was sent), and the other one is placed at the position where the light will hit the train's front clock (the one inside the train, equipped with the sensor), but relative to train tracks; let's say the second stationary observer really needed to repeat the experiment several times to get this position accurately enough.
What do the stationary observers measure?
First of all, two stationary observers check their clocks and the distance between them, and it turns out the speed of light was again $c$. It didn't "add up" to train's speed at all this time, unlike the ball from the first experiment. But they also notice the weirdest of things: while the first observer saw the first train clock to show the same time as his stationary clock, the second observer (seeing the light-beam hit the front train's sensor) noticed that the clock on board the train was out of sync with his outside clock; it seemed to be running slightly slower. When the front was showing 0:20, the outside front clock was already at 0:21.
Which of the observers actually experienced the dilation?
At this point, outside observers conclude that the train observers must have experienced dilation; after all, after reuniting, they will all agree that both back clock met at 0:00, and front clock were out of sync in exactly the same fashion (front train clock at 0:20, front ground clock at 0:21).
But, as it turns out, when moving at a constant speed, no frame is "privileged". For the observers in the train, the two clocks outside the train didn't appear synchronized at all in the first place! In fact, when the back clocks aligned at 0:00, for the train observers, it seemed like the front ground clock was out of sync, and already showing 0:02!
So, from the train observers perspective, it seemed like ground observers experienced dilation, because the out-of-sync clock was supposed to show 0:22 at the moment they aligned.
Why is this so unintuitive?
First of all, relativistic effects are hardly noticeable unless you are observing reference frames moving at near the speed of light, which is something rarely observed in everyday life, by everyday people. Our intuition prefers the "safety and comfort" of the throwing ball experiment, because this is what we can perceive in everyday scenarios.
Next, unless you introduce acceleration, time dilation and other relativistic effects only exist as a perceived difference from observers in different frames of reference. No matter how fast you are moving, if you are moving at a constant speed (i.e. don't experience any inertial forces like the ones you experience when riding in an elevator and it slows down), your clocks, lengths, speed of light, and all physical laws as we know it will behave exactly as always. This is another reason why it's unintuitive; you can never observe any effects of relativity on yourself.