The rise of Twitter has been phenomenal and the service has evolved so sharing message of 140 characters or less is no longer enough for increasingly demanding users. TwitPic is an image hosting service which not only hosts images you upload but also provides a shortened URL ideal for sharing via Twitter.
The iPhone app can be used to quickly upload images already stored on your phone, or you can use the camera to take a new shot. Support for geotagging means that information about your current location can be included. The TwitPic apps works well and does exactly what you would expect it to, but for many people it will simply not be necessary.
There are a number of Twitter clients available for the iPhone and most of them feature integrated support for TwitPic as well as other image and video hosting services. While there is nothing intrinsically wrong with the app, it's just not entirely necessary.