Here is how I always explain it:
Distances in space are way too large to express in kilometers. You end up with very large numbers, which are clumsy and uncomfortable to work with.
So they had to come up with a larger unit to measure space.
For that, scientists turned to light. Now, as everyone knows, light travels faster than anything else in the universe. It travels at 300 000 km per second (i.e. the same distance as 8 times around the world in one second).
So once you have the velocity, it is a simple calculation to get the distance that light would travel in the duration of one year.
You know, Distance = Velocity x Time.
That gives you about 9461227000 km, which is equal to one light year.
Since it would take light a year to travel that distance, it means that if an object is, say, a light year from us, it is emitting light now that we will only be able to see in one year's time.
The light you see now is light it emitted a year ago, so you are seeing the object as it looked like a year ago.
That's pretty amazing, considering that we can see stuff like the spiral galaxy Andromeda with our naked eyes, which is 2.4 million light years away. So you are looking 2.4 million years into the past when you look at Andromeda.