The bounce rate tells you how engaged your visitors are with your site, on a general level.
Clicky's bounce rate is much different from any other service - in a good way. All other services define a bounce as simply any visitor who viewed only a single page. With Clicky, though, our tracking code will continue to ping our servers while a visitor sits on a single page. This gives us a much more accurate picture of how long the visitor was actually on your site.
Our bounce rate takes this into account. A visitor will only count as a bounce on Clicky if they only view a single page and they were on your web site for less than 30 seconds. We figure, if someone is there for at least 30 seconds, they were at least mildly engaged and should not count as a bounce.
IMPORTANT: Because pinging can take up a lot of extra bandwidth, a paid account is required for this to work. Otherwise, our bounce rate will only be based on single page view visits.