Okay, Let's see if I can shed some light on the subject.
First off, it is important to note what Relativity says about velocity and time.
When we say that time slows for an object that travels at near c, it is important to understand just what this means.
Relativity deals with measurements between reference frames. Thus one measures a time rate difference between himself and a frame that is moving with respect to him. If the Relative velocity remains constant, an observer in each frame will measure the other's time rate as slower.
Now here is the part that trips people up:
There is no way to say to choose either observer's measurements as reflecting reality better than the other's.
Both observer's measurement's equally reflect "reality".
Now how does one square this with the Twin paradox, where one twin returns younger than the other?
First we must understand how accleration effects measurements between frames of refernce.
Imagine a space ship accelerating through space. (the astronauts feel themselves pushed to the back of the ship due to this acceleration.)
There is a clock in the nose of the ship and one in the tail, and they are sending time signals to each other.
Because of the fact that light has a constant speed as measured by any observer, the clock in the nose will see the clock in the tail run slower,and the clock in the tail will measure the clock in the nose run faster. How much faster depends on the value of acceleration, and how far apart the clocks are separated. For any given accel, the longer the ship, the greater the time difference measured.
Now, this measurement of different time rates are not limited to items in the ship. If one were to look out from within the ship to a point somewhere up ahead, you would also see the same thing; clocks further ahead of you would run faster than clocks closer. ( and conversely, if you look behind you, clocks further away would run slower. )
Note that this effect is only measured by someone undergoing the acceleration. If you watched someone else accelerate in respect to you, the only time rate difference you would measure would be due to your relative velocity.
Now let's apply this to the Twin paradox. Twin A and B are sitting in spaceships at reart with each other.
Twin B fires his engines, accelerate up to near c, coasts for a while, brake to a stop, turns around and returns.
What Twin A measures:
Twin B increases relative speed wrt himself. As he does so, Twin B's time rate will slow down until he reaches coasting speed, then it runs slow at a constant rate.
He then coasts for say 10 ly, slows down, acclerates back towards Twin A, coasts again, then brakes to a stop next to Twin A. During both coasting periods Twin A will measure B's clock as running slow at a constant rate, and during the braking and turnaround, he will measure B's clock still running slow, but by a varying amount.
When Twin B returns, A will say that B will be younger because B's clock ran slow practically the whole time.
What B measures:
As the velocity between Twin A and himself increases, he will experience the feeling of being pulled to the back of his ship. He can attribute this to two possibilities, either he is accelerating away from Twin A, or A uniform gravitational field has come into existance, and because he is firing his engines, he is standing still, and because twin A isn't, he is falling.
In either case he will measure the following, Twin A's clock will run slow because of the combined effect of Increased velocity difference and the acceleration felt By B. both effects will increase as the velocity and distance increases.
The engines cut out and B coasts for a time. during this period, he will measure A clock as running slow at a constant rate. After traveling a distance (this distance depends on the relative velocity between A and B. I.E. if it is .866c, then due to length contraction, the 10ly measured by A will only measure 5ly for B)
B fires his engines again, though this time in the opposite direction. Thus twin A's position wrt the force felt will be opposite of it was before.
B's decreasing velocity wrt A will decrease the time slowing effect he measures. The fact that he is accelerating towards Twin A will cause him to measure Twin A's clock as running faster. Because The distance between A and B are much greater now, this speed up will over shadow the slow down effect effect due to relative velocity. B will measure A's clock as running consideralby faster.
This will continue after B comes to a stop and accelerates back towards A.
Coasting again, and A's clock is once again seen as running slow.
Braking, and A's clock runs slow due to both effects. (though the acceleration effect is small because the distance between A and B is small.)
After B comes to a stop he notes that more time has accrued on A's clock and A is older. (The period he measured clock A as moving fast more than compensate for the periods it ran slow)
Twin A aged more becuase his clock ran Slow, very fast, and then slow again with the very fast perod predominating.
Thus both twins agree as to who is younger, and by how much, but do not agree as to how this came to be.
And there is no way to choose one Twin's interpretaton of events over the other's. Each are equally valid and "Real". Which one you use depends on whether you are twin A or Twin B.
This is what is meant by "Time is Relative". There is no universal "real" time rate that is modifyed by velocity. There are only the relative time rates measured from within frames, and which one is "real" depends upon which frame you work from.
All that is required is that clocks that are separated into different frames agree as to their respective time differences when brought back into the same frame again. (they don't have to agree as to how the difference came about. )
