Please see the main Continuity website at http://continuity.tlt42.org/
At its core the web uses the stateless HTTP protocol. In a CGI setting, this effectively means that your program is re-started during each instance of user input, losing all current variable values and other program state information. Most applications combat this by keeping track of the current application state in GET, POST, and session variables, effectively implementing an ad-hoc State Machine.
Continuity uses a programming concept called continuations to make HTTP seem like a statefull protocol instead of stateless protocol. This technique is increasingly called creating a Continuation Server. Continuity is a suite of libraries (not a framework) for building a highly structured web-based interface for your application, without using ad-hoc state management. Continuity is Free Software, distributed under the same terms as Perl itself.