Imagine you have a star, B.
1 light year west of B is a star called A. This solar system is inhabited by Aians.
At the same time, 3 light years to the east of B is a third star, C. This solar system is also inhabited, this time by Cians.
Aians and Cians are in radio contact with each other and have been for many decades - it takes 8 years for a signal to make a round trip from A to C and back, but who cares? It's pretty good for an Einsteinian universe with no FTL.
A B C
Suppose B suddenly, unexpectedly, goes supernova. The supernova, let's say for the sake of argument, expands at half the speed of light, while the light from the supernova moves (of course) at light speed.
After 1 year, the Aians see that B has gone supernova.
After 2 years, the supernova shockwave reaches them and - let's say - wipes them out.
After 3 years, the Cians see that B has gone supernova. They know how far away B is, how far away A is, and how fast the supernova is expanding; from this they quickly infer that the Aians must have been wiped out 1 year ago.
(After six years, the Cians are also wiped out, but that's not important.)
Read that again: the Cians know that the Aians have been destroyed just one year after it happens - even though it happened four light years away. That information has travelled at four times the speed of light!
Wait, no it hasn't.
Move C west a light year.
A B C
In this situation, the Cians see the supernova at the same time as the shockwave hits A, which gives the impression that the information travelled three light years instantly.
Move C any closer to B and it looks like the Cians know about A being destroyed before it even happens... and the fault in the reasoning becomes painfully obvious. Nothing - neither information nor matter nor energy - has actually physically travelled from A to C. The inference that A has been/will be destroyed isn't certain until the light of the expiring Aian homeworld reaches C, years later. The actual fact of the matter is rather that all the relevant information was actually at C all along.
The applications of this are limited on Earth, where an electrical impulse can circle the globe in a seventh of a second. But I can imagine this becoming a useful effect in space-based scenarios.
Imagine, for example, we replace A and C with two fleets of slower-than-light starships and B with a central command post, relaying instructions to the two fleets. One could have a situation where fleets A and C - acting on instructions sent from B - are moving in perfect synchronicity, perhaps to rendezvous or attack a certain position together, despite it being physically impossible for them to communicate with each other!
And that's how you can (dupe your enemies into thinking you can) transmit information faster than light, but can't really.