Let’s suppose you hopped aboard a rocket ship, destination 14 billion light years away. This rocket ship has a comfortable constant acceleration of 1g (10 meters per second per second). This rocket ship would approach the speed of light in approximately 347 solar days (your time). At this speed, travel to anywhere in the universe would seem almost instantaneous.
Why? Einstein’s theory predicts both length-contraction and time-dilation at relativistic speeds. When traveling at near-light speed the universe appears, to the traveler, to contract to two dimensions. In other words, it becomes almost perfectly flat. Rather than 14 billion light years away, your destination is practically close enough to touch.
The only problem is that it is a one way trip. This is because of time dilation. While you have been experiencing the sensation of a constant acceleration of 1g, to the folks at home tracking your progress, your acceleration has been decreasing at an exponential rate. If they could see a clock inside the ship, it would appear to be moving slower and slower until it appeared to stand still. By the time you approach the speed of light, your observers, along with the Earth and Sun will have long since died. In their time, well over 14 billion years (my calculus is a bit rusty) will have passed. You will have no home to return to.
*One other interesting aspect of near-lightspeed travel is that mass increases with velocity. As you approach lightspeed, your mass approaches infinity. Some people might argue that It would be impossible to accelerate such a huge mass because of the enormous amount energy it would take. That’s where Einstein’s famous equation E=MC2 comes in. Suppose your ship is using a form of nuclear propulsion. As your velocity increases, so does the mass of your ship and everything on it – including your fuel. As the mass of your fuel increases, so does its energy. Voila! No extra fuel is needed. (Admittedly, this seems to violate the law of conservation of energy but blame Einstein, not me.)