John, a lightyear is a measure of time, as well as of space. Hence the term, "year," an interval of time.
Since you mentioned two people walking away from each other, let me try and explain it this way:
Suppose you and your friend propose to signal each other every ten paces. You start out hollering "hello," and following a number of iterations, you notice that the signal grows fainter and takes longer to reach you. When sound is no longer adequate to communicate, you use flashlights. Now you find that your friend's light beam takes the same amount of time to reach him, as his light takes to reach you.
You determine that you are x light-seconds apart. Space and time appear to be absolute, with a constant speed of light.
That will be good enough for all practical applications; even a relatively complicated task like landing a person on the moon needs no more signalling power than the absolute space and time of Newtonian mechanics. All the phenomena are what relativsts call "timelike separated," meaning that your ordinary intutition of how space and time are supposed to look is not offended.
When we calculate the relativistic effects of cosmic distances and/or velocities, we find that intervals of spacetime look very different to different observers. The "pop quiz" link is by Professor Andrew Duffy at Boston University.
Best,
Tom