Why does the sun have a luminosity of 1?

It really depends on the units used. Sometimes the Sun is used as a comparison for the brightness of other stars, or even galaxies - in this case, the Sun's luminosity is arbitrarily defined as 1, and a star that is 10 times brighter will have luminosity 10, for example. However, if you use other units, for example watts, you get quite different numbers (3.846×1026 watts for the Sun, according to the Wikipedia).