This is commonly illustrated with the following scenario. Imagine Alice is sitting by the train tracks. Her friend Bob comes past riding on top of a train, sitting exactly in the middle of the car's roof. As he passes Alice, they high-five (presumably Alice is on a raised platform of some sort). A split second later, Alice sees lightning strike each end of Bob's carriage at exactly the same moment. Thanks to some very precise measuring equipment, Alice is able to determine that the two lightning strikes occurred at the very moment that she high-fived Bob. At that point, Alice was exactly halfway between the two points that were struck, so it makes sense that the light from those strikes reaches her at exactly the same time.
Alice also knows that Bob would have seen lightning strike the front of the car before it struck the back of it: the light from the front strike would have passed Bob on its way to Alice, and the light from the rear strike would have passed Alice on its way to Bob.
Now let's look at it from Bob's view. As Alice concluded, he sees the lightning strike the front of the car first. But (a) he's exactly the same distance between the two strike-points, and (b) the speed of light is always the same for any observer. So if he sees the light from the strike at the front first, that means the front was struck first. Bob has a different order of events from Alice.
Which order is the "right" one? Answer: both. Or, if you prefer, neither. There are no grounds to prefer Alice's view over Bob's, or vice versa. You cannot say that one lightning strike "really" happened first, or that they "really" happened simultaneously.
To complete the picture, let's imagine Charlie riding another train car on the set of tracks the other side of Bob's, travelling in the opposite direction to Bob. At the exact moment Alice is high-fiving Bob, Charlie is also exactly lined up with them and smacks Bob on the back of the head. For reasons similar to but opposite to Bob, Charlie will first see lightning strike the rear of Bob's car and then the front, which means that in his (equally valid) frame of reference, the rear strike happened first.
Now imagine someone or something used FTL travel to go from the front of Bob's car to the rear, leaving at the moment the front was struck by lightning and arriving at the moment the rear was struck. In Bob's frame, this would be unremarkable, except for the exceptional speed (ignoring for the moment any adverse environmental effects -- Google "what-if xkcd relativistic baseball" for a flavour of what those might be). But in Charlie's frame, this would be travel backwards in time, as the arrival at the rear would occur before the departure from the front.