Friction Pastes, (also known as Carbon Pastes) work by increasing the friction between two surfaces, for example: a seat post and a seat tube. This increase in friction reduces the amount of clamping force that needs to be applied by a seat post clamp for example, reducing the risk of crushing delicate components.
If you've ever tightened a seat post clamp to the maximum torque value only for the seat post to continue slipping you'll understand why you need Friction Paste. Unlike old steel bikes, you can't just crank down on bolt anymore without causing expensive damage. Components are designed to be as light as possible and if you are unlucky enough to damage a carbon seat post, or worse, a frame, the repair or replacement cost isn't cheap.