I've never found a good simple explanation. The basic idea is:
Arrows show motion, close to the speed of light.
A sends to B FTL. In the reference frame of C and D this seems to go back in time.
B sends to D. This takes normal time, but B and D are close.
D sends to C. In the reference frame of A and B this seems to go back in time.
C sends to A. This takes normal time, but C and A are close.
In all reference frames, the message returns to A before it was sent, because everyone sees one big backwards-in-time hop.