Conversion Rate and Bounce Rate are SEO buzzwords that are getting bounced around a lot lately. If you have a low conversion rate or a high bounce rate, you should worry. It's like having too much bad cholesterol or not enough good cholesterol. Conversion rate is directly applicable to commercial online store Web sites and somewhat less applicable to other websites. It measures what proportion of your visitors actually bought something or did whatever it was you want them to do. Bounce rate is supposed to measure how many visitors got to your web site and said "this is of no interest" and left. In actual practice, there are two pretty iffy ways of measuring Bounce Rate. The first measures the time that visitors spend on a single page. Obviously, if they are only spending a few seconds on a page and leaving the site, they might be uninterested in your site, or else they might be robots or they might be people who get to your page and find what they want and leave, or people who click an external link or another link in your site. It all depends you see. Of course, a visitor might get to a page, decide it is worthless and go get a cup of coffee or read e-mail. So pages that are open for a long time don't always mean what you think. The other measure of bounce rate is how many people get to your site, view only one page and skedaddle. They might not like what they see there, or they might have gotten exactly the information they need and they are out of there.
Suppose you have an informational Web site. If I want to look up Abraham Lincoln's date of death, I should be able to get to that page in your site from Google, get my information and be gone. I'm happy. If I have to go to the main page of your site, click on "Famous People" click on "Presidents of the "US" and then click on "Abraham Lincoln," your site design is terrible and your optimization is worse. Your visitors are unhappy, but Alexa and similar tools will show that you have a lot of "depth" and a low "bounce rate" because each visitor generates 4 pageviews.
Moral of the story: Make sure you know how someone is defining a term, and how they are defining the term before continuing. If they haven't defined it, then what they have to say is often not interesting or generates more confusion than understanding. When evaluating claims about how search engines rank pages, consider the real world problem that search engines have to solve for all kinds of websites, not just commercial sites that are the model that most seo "experts" have in mind. Not everyone is ebay or Amazon. If it is really true that search engines like Google are using Bounce Rate (in the sense of depth of visits) as an indiscriiminate criteria for ranking all websites, they are making a mistake. It might be useful for sites of certain kinds, but less useful for sites like Wikipedia, where people may spend 20 seconds on a single page getting a single fact they needed. I didn't see any dip in Wikipedia rankings, did you?