Time Dilation
According to Einstein's Theory of Special Relativity, clocks on rapidly moving spacecraft will advance more slowly than stationary clocks. This applies to all "clocks" (mechanical, atomic, biological).
For example, a clock on board a spacecraft moving at 99% of the speed of light will appear to be advancing 7 times more slowly than a clock at rest (see formula on page 472).
This means that astronauts age more slowly than do we who remain on Earth ("the Twin Paradox"). Example: Trip to Alpha Centauri (4.3 light-years) at 99% of the speed of light would take 8.7 Earth years, but the astronauts would only age by a year and 3 months!
If humans were willing to return to an Earth populated by their descendants then voyages across the Galaxy might be possible.