What does being a Kohan symbolize? What does it mean?

Answer 1

Temple Priests
In the days of the Temple in Jerusalem, Kohanim (plural for Kohen) were priests responsible for worship ceremonies, such as leading services, offering sacrifices, burning incense and more. To maintain a high degree of purity, Kohanim observed certain prohibitions concerning marriage and contact with the deceased.

The High Priest, called HaKohen HaGadol, was the head of all the priests. He conducted services in the Temple on Yom Kippur, the holiest day of the Jewish year. And he was the only person allowed to enter the Holy of Holies, the holiest place in the Temple.

Today a Jew is considered a Kohen if he is a descendent of the first priest Aaron, the brother of Moses, from the Levi tribe.

Answer 2

Kohan is the most common family name in Judaism that has direct connections to the Levititcal priesthood, as I understand it.
With the name (should) come knowledge of the traditions and rituals of the Jewish culture.