First of all you create a basic landing page or website.
Let's say you wanted to see if using a different sales copy would lead to more sales.
You would then enter your various sales copies at google adwords and copy a bit of code into your webpage both on your landing page and on your contact/thanks for buying page.
From now on, whenever your website appears it will randomly show a different sales copy.
Google will then show you which sales copy brought you the most sales.
After a while of testing, you might decide to stop the experiment and just use the best sales copy.
I hope that explains it. If you have any questions, don't hesitate to ask.
You're explaining a feature called "WebSite Optimizer" which is different than "Conversion Optimizer."
Conversion Optimizer automatically manages your bids based on historical information about keyword/site/ad group conversion rates, attempting to optimize the volume of conversions you get at a target CPA that you give it. To use CO, you need 200+ Adwords-tracked conversions in a given campaign, and if you have that, you'll find an option on your bid management pages to enter in a CPA target. If you don't have that volume of conversions, you can try moving your conversion code higher up in your conversion funnel, which will increase the volume of your "conversions." You'll still need to track the volume of people that come through your previous conversion point, but this change will help you automate your bid management, and allow you to spend more time focusing on other aspects of your campaign.
Does that help? Your explanation of Website Optimizer is spot on, and the two features can both be helpful.
Ultimately, though, you can try it yourself and see how well it works on your campaigns. To be eligible, you need to have set up conversion tracking through Adwords, and if you've done that - and have more than 200 conversions/mth - it should be pretty easy to set the CPA bids on your campaigns or ad groups.
Let us know how it works for you.