I'll just quickly explain a few terms I’ll be using for those of you who haven't taken any advanced physics course.
World-line = Imagine an object moving at a constant speed from an origin, if you were to plot its position on a distance-time graph, it would trace out a straight diagonal line from the origin, this diagonal line is its world-line. If the object undergoes an acceleration at any point during its journey a curve would appear in this line.
Frame of Reference = Imagine you are travelling in a car at constant speed, if you were to measure the speed of another car you passed by, you could only measure the difference in speed, i.e. if you were travelling at 70mph and the other car 60mph you would measure its speed as 10mph. However a person standing on the bank would measure the correct speed as 60mph. Therefore how we perceive the world is totally dependent upon the Frame of Reference we compare it too, in this case we take a person standing still in space.
I might use some other terms during the explanation, if anyone has any problems understanding what they mean, don't feel stupid and ask, I had to many times.
For those of you not aware of the twin paradox here is a quick re-cap from my notes, I'll include pictures.
"Consider two twins who start from the same place in space and head in the same direction, twin A experiences no acceleration and his world-line is therefore straight. Twin B, on the other hand accelerates away from twin A for a short period and then undergoes inertial (constant) motion. After a certain time twin B decelerates until they are approaching A again with the same velocity as that with which they were originally going away from A. Finally twin B decelerates until they are at rest with respect to A (going at the same speed). Twin B will now surprisingly find that they are now somewhat younger than twin A, if they were to repeat the experiment several times, travelling at the same speed each time, they would find that the relative amount by which twin A ages is proportional to the length of Twin B's journey."
See below pic for a better idea.
Funny eh? its been proven with atomic clocks on placed on Jets that were flown round the world and then compared with those that stayed on Earth.
People have argued that the you could equally take Twin B to be standing still while twin A travels away in the opposite direction, reverses and comes back in respect to twin B's frame of reference. The paradox occurs because looking at it this way there would be an asymmetry between the measurements of the two twins. Twin B would be younger having not moved.
However this argument falls down when we consider the effect of acceleration on the frames of reference, twin A's journey is inertial, in that they don't experience any acceleration, they travel at a constant speed all the time. However twin B will experience acceleration 3 times during their journey, this is more than just relative motion with respect to twin A, twin B will be able to detect the force of the acceleration on themselves even if they were unable to see A. The argument of the twin paradox breaks down here.
One way to look at this argument is by using 3 different observers and split the journey up between them, see below.
Using this approach we can look at the problem without having to consider acceleration which can often complicate matters.
Observer B is receding from A at a speed greater than that of A's, similarly, C is approaching A at the opposite speed of B. A and B met at event F and synchronise their clocks, B and C then intersect at event E where C synchronises their clock with that of B.
Then when C and A finally met at event G and they compare clocks the same difference in time will be measured as in the first case where twin B had experienced less time than that of A.
And that is the answer to the twin paradox.
I'm actually finding explaining this stuff to other people is helping me understand it a lot better...any problems let me know.