Bounce Rate is the number of visitors that land on a page/site and leave before navigating any further. Exit Rate is the number of visitors that leave your site from a given page based on the number of visits to that page.
Why are they important?
Bounce rate will tell you if your content is interesting enough that people have visited your site and stayed. For eCommerce sites it will tell you if your offers are good enough, your site trustworthy enough, or your products enticing. For other sites it will also give you signals of trust. There is also some evidence that it is used as a quality signal by Google. This may or may not be true, but we do know that if a user searches for something, visits a site, and then bounces right back to Google, they get the option to block all results from that domain from their search. This data is also being used in Google’s algorithm to detect quality.
Exit rates will tell you if people are leaving a particular page and not going any further. They matter because they will tell you if a particular page is turning people off, or if you have an eCommerce site, where people are leaving that site. If you have high exit rates on your shopping cart, it means people don’t trust you, your shipping costs are too high or they changed their mind.
High exit rates on some pages is not a bad thin, after all some people have to leave your site at some point. High exit rates on sign up or conversion pages might be a bad thing, if you are trying to get people to do something.