The answer comes from its spiritual symbolism
In the early centuries of the Church, priests did not wear anything distinctive for their everyday attire. They wore the typical clothing of the period and would only look different when they put on priestly vestments for celebrating Mass.
Over time the fashion trends shifted and instead of moving along with the rest of the world, the clergy retained the former way of dressing. It was during the 12th and 13th centuries that priests adopted the Roman cassock as the piece of ordinary clothing that distinguished them from the laity. Soon after this decision the Church made further regulations that required priests to wear the distinctive garb.
At first the cassock only consisted of a robe-like garment tied at the waist with a sash and did not feature a white collar as we are familiar with today. The color of the cassock did not receive regulation until much later and likely rose from the easy availability of black dye. Historically black was the cheapest dye to use and so was fitting for the simple parish priest. Other clergy members wore different colors to distinguish their rank and around the time of Pope Pius V, the pope began to wear a white garment similar to the pope’s white cassock today.
The black cassock is still a garment worn by many priests, though most bishops’ conferences around the world have permitted the use of a black shirt instead.
Symbolically black is associated with simplicity and humility and reminds priests of their need to imitate those virtues. Black is also a color that represents death and mourning and symbolizes how a priest is to die to oneself and decrease so that God may increase in his life. He is called to take up the cross of Our Lord daily, dying to sin so that he may rise in the life of grace.
While it is true that parish priests are required to wear the color black, in hotter locations, dispensations allow priests to wear a more tolerable white.
Nevertheless, the distinctive color of the priest’s clothing sets him apart from the rest of society. It reminds us of his mission to serve and signals him out in a crowd of people. The presence of a priest is supposed to point our hearts to heavenly things and brings the person of Christ to each one of us. The color simply highlights this reality and should provide a kind of “mini-homily” every time we see a priest.