Transactions are more or less complex process which can either be committed (thus changing the state of the system) or rolled back (thus restoring the original state of the system).
The challenge typically faced in "web" based interfaces is that the HTTP protocol, on which the web is built, is stateless, i.e. a "basic" web server cannot distinguish between a "new request" (starting a new session) and a response to an earlier request (continuing in same session).
Cookies and/or cleverly generated links and/or hidden form fields solve this problem. They either keep the session state on the client or on the server and thus make it possible to "remember" sessions transmitted over a "memoryless" protocol.
So "designing transaction flows for the web" entails more work than, say, a simple dialog box or a multi-page assistant with "Cancel" and "Ok" buttons in a "normal" desktop application.