Albert G. Mackey explains the importance of the apron in Masonic thinking.
Albert G. Mackey, An Encyclopaedia of Freemasonry and Its Kindred Sciences (Philadelphia: Moss & Company, 1894), 83–84
Apron. There is no one of the symbols of Speculative Masonry more important in its teachings, or more interesting in its history, than the lambskin, or white leather apron. Commencing its lessons at an early period in the Mason's progress, it is impressed upon his memory as the first gift which he receives, the first symbol which is explained to him, and the first tangible evidence which he possesses of his admission into the Fraternity. . . .
In the Masonic apron two things are essential to the due preservation of its symbolic character — its color and its material.
1. As to its color. The color of a Mason's apron should be pure unspotted white. This color has, in all ages and countries, been esteemed an emblem of innocence and purity. It was with this reference that a portion of the vestments of the Jewish priesthood was directed to be white. In the Ancient Mysteries the candidate was always clothed in white.