Preservatives function to maintain a long shelf-life and consumer use period, of generally >2 years. They kill bad bacteria that comes into contact with the product through light, air, or repeated touch.
While they're there for the product, they are harmful to skin. They kill any good microorganisms your skin has and needs, throwing your skin into imbalance and stress as it tries to recover. And it happens every time you apply any preserved product - which includes all current moisturizers and cosmetics on the market. They're also well known skin irritants and sensitizers, and lead to many skin conditions with repeated use.