RStudio, the folks behind the IDE for R released last year, continues to expand their offerings for current and future R users. Shiny is RStudio's most recent release, and it aims to make R web applications easier to make and share.
However, don't get too excited about R on the Web yet. The apps are meant to run locally, so to share an application with someone, you have to send them the code for them to run on their own. RStudio is working on a paid service that lets you host your apps online. Or, because Shiny is open source, you can try running it on your own, if you like.