Each page created gets its own URL, which visitors can revisit any time and watch once the live streaming part is over.
Regarding the chat, it's all supported via tweets. Anytime anyone replies to your tweets where a link to your show is included, the application counts it as a reply. Then it aggregates them in a place, so that everyone who watches the show can see the entire conversation. It is not exactly the best way to tackle it, since sometimes it is nice to have some basic text chat that doesn't fill your Twitter stream with stray tweets, but it is done in a way that keeps everything compactly-organized.
Livestream says “Twitcam was built in about a week & uses new player tools that are going into an updated version of its API that will be released in the near future. The company hopes these will let anyone build a similar service with their own branding, and audience tools--preferably with a chat system that does not require so many tweets.”
I tested this app but my bad luck, the faulty webcam didn’t allowed to shoot my first show. ALAS!
Would be updating once I’ll go live with my TwitCam.
See also: Justin.tv's CamTweet (which is in private beta)