When a people is separated, they are positioned apart. To be Set Apart is to be put into a specified position.
The Priesthood of Yisrael is a separated position. They are called to teach about Torah. The book of the law can not depart out of their mouths. Malaki/Malachi 2:7 For the lips of a priest should guard knowledge, and they seek the Torah from his mouth, for he is the messenger of YHWH of hosts. Malaki/Malachi 4:4 Remember the Torah of Mosheh, My servant, which I commanded him in Horeb for all Yisrael-laws and right-rulings. Psalm/Tehillim 4:3 But know that YHWH has set apart him that is godly/kind for himself: YHWH will hear when I call unto him.