This clearly reveals a lot about Zach's character and how he views the issue of racism in his world. For him, the solution to racism is not about trying to act white or to blend into a white world or even to withdraw from it completely and life segregated lives where blacks can live without fear and in peace. Zach understands that the only solution to the issue of racism is to change the entire world and the attitudes that have created racism in the first place.
This is obviously a very radical solution and it clearly shows the commitment that Zach has to change, no matter how difficult. It also seems to foreshadow the Civil Rights movement and their battle for equality and their refusal to live in a world that was shaped for them by whites any more. This quote tells us that Zach is a passionate, principled and committed individual who sets himself to do what is right no matter how hard or challenging that path may be.
Zach says this to Lily because in their world of South Carolina in 1964, an interracial couple is an impossibility. Zach is black, while Lily is white, and Lily dreams of becoming black so she can be with Zach. Instead, he wants to change the world by becoming a lawyer and fighting for social change.
Lily says that the events of 1964, including the riots in New Jersey and Malcolm X's philosophy of direct confrontation with whites, have affected Zach and made him angry. She says, "coming into his presence was like stepping up to a gas heater, to a row of blue fire burning in the dark, wet curve of his eyes." Zach is impassioned and dedicated to pursuing social justice. He is intelligent, informed, and committed to changing the world so that people can love who they want and be who they want, no matter what the color of their skin, and he has the drive and commitment to pursue what he imagines.