Imagine you are standing still by a road and a car passes you at 60 miles per hour. Now imagine you are in another car traveling at 58 miles per hour and the same car passes you. Your speed means that the car will appear to only be traveling at 2 mph - you can even look over and talk to the people in the other car! In fact, we are all traveling at around 800 mph as the Earth spins but because we are all moving at the same speed, we don't notice. But what has this got to do with time in space, you may be wondering? Well it's all to do with the speed of light.
Light travels at 300 million meters per second regardless of what speed you are traveling. Unlike the apparent speed of the car discussed above, which is dependant on how quick you are travelling yourself, light always appears to travel at the same speed relative to how quick you are going. If you're going at 1 mile an hour or 1 million miles an hour, a passing light photon will still be going at 300 million meters per second relative to you. This might sound odd to you - it does to me too. It was this weird phenomenom that led Einstein to propose his special theory of relativity in 1905 - a theory that hasn't yet been disproved but is highly controversial among many. He stated that, rather than living in a 3 dimensional world, we actually exist in 4D space-time, which includes the 3 dimensions of space, plus time. He proposed that the sum of velocities in these 4 dimensions will always equal the speed of light.
To put it another way, the closer you get to the speed of light, the slower time becomes. This leads to the interesting Twin paradox in which one twin remains on Earth while another is sent off into space at close to the speed of light. A mathematical formula known as the Lorenz transformation takes into account the speed at which you are moving to determine how fast time will pass. In the case of the twins, if one travels at 95% of the speed of light for 10 years, he will return to Earth to find that 32 years have passed for his brother. Doesn't sound right to you? I admit it is all a bit odd and it gets even stranger if you start trying to explain it all. If you want to know more about this then try: http://science.howstuffworks.com/relativity3.htm, I'm not going to get into it all now! This is effectively time travel, but there are just a few problems. Most importantly is that we can't actually move anywhere close to the speed of light. Moving at the speed of light would increase your mass to infinity and would make it pretty much impossible to move at all!
Einstein's special theory of relativity didn't take into account gravity, so he proposed his General theory of Relativity in 1915. This is a bit hard to explain and I'm not a physicist so I don't want to get it wrong and confuse people. Basically, general relativity is a theory that relates to the behavior of space and time. In the theory, space and time are dynamic in that they can be curved by matter. Imagine this like a bowling ball resting on a trampoline, where the trampoline is space-time. It also explains gravity in a different was to that proposed by Newton. Instead of being a force, gravity is a result of the space-time curvature caused by a large body such as the sun or a planet. This theory explains various phenomena that Newtonian gravitation has problems with - like the exact orbit of a planet around the sun or the bending of light by gravity. For a good explanation of general relativity, try http://www.ncsu.edu/felder-public/kenny/papers/gr1.html
Another thing to consider is the effect of being in space on an astronaut. It depends on how you think of ageing. I don't think you can consider age as a function solely of chronological age. Ageing is pretty much deterioration of the body over time but it depends on all the stresses you put on it. Going into space is really tough on the body, and in fact long periods spent in space have a similar effect on the body as normal ageing on Earth does. Experiments on earth have shown that subjects who lie down for a long time to reduce the amount of gravity they experience end up with symptoms similar to the elderly who live in nursing homes. So age isn't as much to do with the passage of time, but the amount of exercise and movement that the body does. On Earth, gravity does affect us by causing us to wrinkle more, and in space the lack of gravity will initially allow us to move more easily as our mass is effectively less without gravity. However, in space, the lack of gravity leads to bone and muscle deterioration and the heart gets lazy as it doesn't need to work as hard. This results in lots of astronauts fainting upon returning to the normal gravity of the Earth and finding it pretty difficult to walk. In addition, astronauts are exposed to 10 times the level of harmful radiation that we experience on Earth and during solar storms; the levels of radiation can be equivalent to hundreds of chest x-rays. The effects of microgravity on the human body is an interesting line of research due not only to the predicted benefits to astronauts if we can prevent the harmful effects of living in space, but also because it may tell us more about normal ageing on Earth.
So in summary, even if you could travel at the speed of light
and make time move more slowly, going into space is so stressful
on the body that you probably wouldn't live any longer than anyone
who'd spent years extra on Earth.
