Each is used to measure the very large distance in our universe.
Explanation:
The AU or astronomical unit is the shortest distance of the three. It is the rough distance from the sun to the earth but since our distance to the sun varies from about 92.5 million miles to 93.5 million miles it is not exact. The average, 93 million miles is used. The AU is used strictly to measured distance in our solar system.
The next distance is a light year. A light year is the distance light travels in one year. Light travels at 186,000 miles per second. Multiplied out that means light travels roughly 6 trillion miles in one year. The nearest star is about 4.22 light years away. That comes to roughly 25 trillion miles. The distance in trillions is simply to great for the human mind to grasp and overburdens computers when doing measurements.
Finally there is the Parsec. It is equal to about 3.26 light years. A parsec is a very complex idea. Basically it is used to measure the distances between any two objects beyond our solar system. It is complex because it takes into account the movement of the earth relative to those other two objects to better define the desired result.