I break conversion optimization into two parts:
You can do all of the work in the world to make sure that your pre-checkout information (homepage, product pages, marketing collateral, etc) is absolutely outstanding, yet still, you’ll often suffer from poorer results than your site is capable of.
Checkout optimization is very different from typical page (i.e. information) optimization. You’re no longer trying to inject new information into the flow, you’re trying to minimize friction and overcome latent trust issues with shopping online. You’re also trying to deliver on and reinforce the promises you made previously in the browsing session.
In many ways, much of this work is aimed towards new customers — but it benefits existing, repeat customers as well.