Affinities are the three main ways that your civilization will stand out; the Affinity that you have the most XP in will be the one your opponents react to.
The Harmony Affinity is about taking the Human genome, and strengthening it with alien DNA from the planet, and adapting with the planet to call it "home". This eventually leads to units that are Human/Alien hybrids, a culminates in the Mind Flower victory condition, where you achieve shared consciousness with the planet, or "Transcendence Victory".
The Purity Affinity is about maintaining the sanctity of human life, and using ever-more-powerful mech-suits for its infantry. This Affinity culminates in the Promised Land Victory, where a Warp Gate is opened back to Earth, and refugees are led through it to make a new life on the planet.
The Supremacy Affinity is about artificially strengthening humanity, often with cybernetic or robotic implants or attachments. This Affinity culminates in the Emancipation Victory, where you open a Warp Gate back to Earth; however, instead of leading people through the gate to begin a new life, your forces enter it, and conquer the Earth, uniting it under your rule.