Before you can understand this concept, you have to understand why time dilates and space contracts for observers in different intertial reference frames (i.e., one observer moving at some constant velocity relative to the other.) I suggest looking at the videos for The Mechanical Universe, put out by CalTech in the 80's (do a Google search ;)), episodes 42-44.
Everything can be explained by doing Einstein's famous thought experiment about a pair of observers, one on the ground, and the other on an open boxcar on a superfast train, each with a "light clock" - i.e., a pair of mirrors in which light reflects off of each back and forth, such that since the speed of light in a known constant for all observers, the measuring of each reflection is like the tick of a clock. Each observer sees the light in his light clock go up and down, but sees the light in the other's light clock travel diagonally, which because there is more distance that is measured (but with the same speed of light), there must be more time measured relative to what the other observer measured.
Similarly, the observer on the ground can measure (i.e., using his own clock & yardstick) the speed of the train and the distance between 2 posts along the train track - which of course are stationary in his inertial reference frame - while the observer on the train can also measure (i.e., also using his own clock & yardstick) the distance between the posts, and the speed with which they are hurtling toward him, concluding that the distance between the posts must be the product of that speed and the elapsed time on his clock. But since the speed that the observer on the ground measures the train moving is exactly the same as the speed that the observer on the train measures the posts hurtling toward him, since the observer on the train measured a certain fraction of the time that the observer on the ground measured, the observer on the train must have measured the distance between the posts at exactly the same fraction of the distance that the observer on the ground measured, so the yardstick of the observer on the train must be perceived by the observer on the ground as being contracted relative to his own. (And of course, all this time, the observer on the train is looking at the clock and yardstick of the observer on the ground and perceiving that to be dilated and contracted by that amount as well.)
So the yardstick of the observer on Earth that measured, e.g., Sirius at 8 light years away, would be, as measured by the yardstick on the rocketship to be about 1/365th of the length of his own yardstick, so therefore using his own yardstick, Sirius is only about 8 light-days away, and is hurtling toward him at virtually the speed of light (i.e., as measured by his clock & yardstick), so it ends up reaching him in ... 8 days. But that 8 light-days measured by the observer in the rocketship is still 8 light years as measured by the observer on Earth - who BTW sees Sirius as being stationary, and the rocketship hurtling toward Sirius at virtually the speed of light, and thus sees him actually reach Sirius in ... 8 years.
