What about for those who have done neither?
The basics, as I understand it, are these:
According to special relativity, there is no "one" measurement of space/time that is correct. Instead, there are any number of reference frames.
Most importantly for this discussion, time is not universal in all reference frames; hence the phenomena of time dilation you've probably heard of.
However, time flows normally for each reference frame; if you fly away from Earth at relativistic speeds, to you its Earth's time that is slowing down. From your frame of reference, there's no distinction between you moving one way and the Earth moving the other way.
All of these reference frames are correct.
Then comes the problem:
FTL travel, alone, does not violate causality; IE you could fly to alpha centauri with your hyperdrive and fly back, but you wouldn't arrive before you left.
A combination of FTL and STL travel, however, can result in an arrangement of reference frames so where a signal (or, in the case of an ftl ship), arrives before it left.
Imagine you fly away from Earth at relativistic speed. To you, time is passing slower for Earth than for you. After a day, you use your neutrino ftl communications to tell them you forgot to turn the oven off. Since (from your reference frame) time is passing slower for Earth, they receive it in 12 hours. They turn the oven off, then send back a message that they have done so. However, from their frame of reference time is moving slower for you than it is for them, so you receive the reply 6 hours after you left; 18 hours before you send the original message.
There's a more in depth (and probably better informed) explanation to be found
hereEdit: Or as it was once explained to me: "The Universe works like this: Special Relativity, Causality, and FTL travel: pick two"