Time travel is unlikely to ever be a possibility for macro-sized objects, like humans. But, there are several exceptions to this.
The most famous is the 'twin paradox', whereby one twin goes off in a very fast rocket at nearly the speed of light. He then returns to Earth after what his watch says is a few weeks later. But on visiting his brother, he finds he's been buried for decades! Relativity predicts, and this has been experimentally verified, that clocks travelling at high velocity - that is, real time - runs more slowly RELATIVE to a clock (time) that is not moving. Whilst the Earth IS moving as several km per second in its orbit, it isn't remotely near a fraction of the speed of light, so it can be taken to be stationary for this argument's sake.
According to relativity, if you travel through a spatial dimension at close to the speed of light, then you will be travelling through the fourth dimension (time) more slowly. As a crude analogy, it's a bit like only having so much energy to do something; if you use a lot of energy to wash the dishes, you haven't enough to cook that evening's meal!
There are other interesting quirks. A photon, or particle of light, moves at the speed of light in whichever medium it happens to be travelling through (the speed of light is different in water, air, space, glass, etc.) In one very real sense, the photon's time, according to our clocks back home on Earth, has completely stopped; it COULD be thought that the photon exists in a non-time, where all that is and all that ever has been exists in a chaotic, simultaneous, and single moment. Such effects are also seen near black holes, where the infinite gravity slows clocks to infinite slowness.
There is so much more that I'll really have to come back another day, preferably when my son isn't sitting on my lap with a heavy cold. The length of the day, in my frame of reference, is very much relative to how well-behaved my kids are!