I have often come across this Google analytics question- what is the difference between bounce rate and exit rate?
Here is the simple explanation of the question.

Bounce rate is the percentage of people who exited from the page on which they landed. This can be better understood with an example. Suppose 100 visitors on site landed on page A and without checking other pages on the site, 40 people left the website. Technically we say 40 /100 people bounces off the site or bounce rate of the site is 40%.
There can be multiple factors for the bounce. It can be due to visitors landing on page which is not relevant to the keyword through which they reached the page. Or the page design  or visitor couldn’t find what she was looking for?

There is no standard set for high or low bounce rate and this would vary from site to site.  Based on your industry patterns, one should keep eye on bounce rate and try to reduce it.

Exit Rate is the percentage of visitors that left the page out of the total number of visitors that page has received. The difference compared to bounce rate is, an exit rate visitor might have come to the page from another web page on your site then exited your web site. For example a visitor landed on page A and moved to page B and then left the website.

This is critical to analyze in case a particular page of your site has very high exit rate.   Though both the metrics are different, it is extremely important to keep analyzing both these factors.

Low bounce rate and exit rate means customers expectations on your site are perhaps in harmony with your offerings on website.