The number of users who come to your site and take no action divided by the total number of users who come to your site. You could also replace "users" with "visits" as some people do and refer to "bounced visits".

maroonblazer defines it correctly, but the layperson gist is: bounce rate represents the percentage of people who do NOT stick around on your site; they just stop by, and then "bounce" (as in, leave too soon). Since it is expected for site operators to want to keep people engaged on your site, you want the bounce rate to be as low as possible (which would mean that more people are sticking around on your site).