This question already has an answer here:
I have heard that time-travel is possible...relative to some observer.
So, as I understand it, the following example would be accurate:
There are two twins- TwinA and TwinB. Both have very accurate clocks, that are exactly synchronised. TwinA leaves earth on a rocket, which travels at approaching the speed of light. After he has counted 24 hours, he comes back to Earth, only to find that more time has passed there, and his clock is now behind TwinB's.
However what confuses me is that speed is relative. So who is to say that TwinA was the one who was moving fast?