A light year is the distance light travels in one year which is:
(Please note, those are American 'trillions' - 1012
When dealing with such distances, traditional units of distance just don't work.
With astronomy distances become really big really fast. In the late 1800s, people actually started measuring the distances to things that are a ways away. This required two things to happen: optics powerful enough to reduce the error and photographic plates to store them on (the photographic process was undergoing a major revolution in this time too).
With this came the advent of the "parsec" which represents a parallax of one arc second 6 months apart. One second is one 60th of a minute, which is one 60th of a degree. Using this notation, Alpha Centauri has a parallax of 0.76 seconds and thus is 1.33 (1/0.76) parsecs away.
The parsec is often used in science but lacks two things - how long has the light been in transit, and popular appeal. Most people just don't understand what a parsec is and it would take some significant work to explain parallax to them. Thus, the light year - some claim that this term was invented by Hugo Gernsback for just this purpose though Webster claims that the word has been in the English language since 1888.
Whatever the case, the distance to the nearest thing outside our solar system is Proxima Centauri - about 25 trillion miles. At this value, things start to become meaningless. Lets talk about the distance of across the galaxy which is 20,000 times that value (or to Andromeda, another 30 times that distance, or to the center of the virgo cluster, another 30 times)- it just doesn't have any meaning to a person... and these things are in our cosmic neigborhood! The other side of the Milky Way galaxy is 100,000 light years - now that is a number I can deal with and gives me some idea of how far.
As science and technology has increased so has the unit of distance. Today, astronomers talk about things in distances of kiloparsecs (3,260 light years) and megaparsecs (3.26 million light years). There is nothing observable that is a gigaparsec away, and nothing can be more than about 10 gigaparsecs away.
The biggest advantage of the the "light time" units are that the "now" that we perceive them represents their state then. Looking at a star such as Betelgeuse in Orion's shoulder I am looking at something about 1500 years old - it is 8.8 quadrillion miles away... and that's fairly close compared to other things.