"Affinities in Beyond Earth are sort of visions for the future of mankind," says McDonough. These are civ-wide philosophies that come in three different flavors: Harmony (humans should alter their genetics to adapt to alien worlds), Purity (people have the right to reshape the world in order to make it most amenable to humanity), and Supremacy (the belief that augmentations and cybernetics are tools to overcome one's environment). Besides informing the aesthetic of a given civ's cityscape and leadership, your Affinity can also determine how you attain victory.
Two win conditions are Affinity-neutral: Domination, where you're the last civ standing, or Contact, the pacifistic win condition where you make first contact with an ancient alien race. Then there are Affinity-specific grand projects. Harmony gets Transcendence, where you awaken the planet's latent sentience ("an homage to Alpha Centauri," says McDonough). Purity has Promised Land, where you reestablish contact with Earth and fulfill your mission to find a new homeland for humanity. Supremacy gets the opposite side of that same coin in Emancipation, in which you decide that Earth's population is hopeless--so to usher them into the future, you send a sizable army back to Earth for a hostile takeover.