Well, it's a little more complicated than that.... but, here's the gist:
When you go faster, time for you *slows down.* So, someone who's stationary, say, you're twin brother on the Earth, will age at a speed everyone here is used to. But, you get on a spacecraft and head off to, say, Alpha Centauri. As you go faster and faster, and get closer to the speed of light, time for you begins to pass more slowly. *YOU* don't know it, really - you look at your watch, and it's ticking along like normal; but, you get to Alpha Centauri, take a few pics, then come back to Earth. Say along the way your speed increases to 90% of the speed of light.
Finally, you arrive back on Earth, after a long journey... As you see it, you've been on that spaceship for almost 29 years. But, when you step out of the ship, and expect to see your now 29-years-older twin brother greeting you, instead it's his grandson - and he's middle aged. While 29 years have passed for you, about 85 years has passed for people of Earth.
Because you gradually built up speed to 90% of the speed of light, (and then slowed down when you got close to your destinations), time for you passed slower than those who were stationary on the Earth... You haven't really skipped into the future, but to you it may seem like it... what happened was time for you slowed down, and the future got here faster (by your view...)