When doing special relativity, the assumption is that everyone has their own personal clock. Due to this, the rate at which time passes for you according to you never changes. One second seems like one second to you. However, you will observe others' time to be moving different than yours. One of their seconds might seem like several of your seconds. Even if you don't pass the speed of light this is true. therefore, what the math states is that beyond the speed of light, you would observe others' time (the people going slower than light in your reference frame) to be moving in a reverse fashion.

However, much like the mathematical solution says that there's a possibility that the height of a swing increases due to friction as it continues swinging (instead of decrease due to friction like we usually see), we consider both of those cases (the swing as well as the past time travel) to be the "time-reverse" of what is the real physical answer. In the case of the swing, if you reverse time for the growing solution, you'll see a dying solution where it swings lower with each swing. The special relativistic case of going faster than light is just a reversal around the speeds between infinity and the speed of light, instead of 0 and the speed of light (notice that 1/0 approaches infinity. Therefore it's a reverse around the fraction of the speed of light you are traveling). Due to the mathematical formulations scientists like to use, you can take time to be (-1) x time and it will provide no new information. But we never observe those things in nature. And so scientists believe that it's just the same solution with t -> -t in the math, and not something real that can happen.

I think the place you heard that was Star Trek. Their physical understanding is frequently wrong.

In Einstein's theory of general relativity, space-time continuum can be visualized as a four-dimensional hyper-surface existing in a five-dimensional space,just as the surface of the Earth can be visualized as a two-dimensional surface in a three-dimensional space. On t his surface, three of the dimensions are what we know as space; the fourth is time. The curvature of space-time is caused by the presence of mass, and the converging curvature of different points is what we know as the force of gravity. Just as an object traveling along the Earth's surface follows a curved "geodesic" path, so must an object in space follow a curved path in space and time. The reason why you can't go faster than light has to do with the fact that hyper-surface of space and time cannot connect two points in space without a certain distance in time between them.

Science-fiction writers and some physicists have speculated that it might be possible to bore a hole through the fabric of space-time and move freely through this five-dimensional space, then you could travel anywhere in space and time at your leisure. The simplest way to envision this is to create a tube-like surface connecting two distant places in space and time. This hypothetical tube-like shape of space-time is called a wormhole. If you were to travel through a wormhole, then you would experience time passing as you travel through it according to the length of the tube in the time dimension. Other means have also been envisioned, however.

No wormholes or other means of traveling not in space-time have ever been observed, although quantum physicists theorize that they do exist at extremely small spatial and short temporal scales (about 10^-33meters and 10^-41 seconds). These also remain unobserved, but the grounds for suspecting their existence is that the theory of Einstein does not agree with quantum mechanics, so one of the theories must be wrong where the two physical principles intersect. If theoretically, you could depart from space-time, then you could travel into the past - or into the future -at any speed that you desired.

Most science fiction treatments of time travel assume you're in a "bubble" of some kind (a ship in a warp field, etc.). If you're inside the bubble, time moves normally: clocks appear to move correctly, a dropped glass breaks, etc. But if you're inside looking outside the bubble, the rest of the universe would seem to be running backward toward the big bang. And similarly for an outsider looking in: life in the bubble would seem to happen backwards.

How to generate the bubble and propel it faster than the speed of light is... um... a "nontrivial problem."