I was made first aware of the WolframAlpha project by a couple of colleagues who were looking into artifical intellgence and were really impressed with this new search engine that could understand questions and respond back with natural responses. As of right now, all search engines have a tough time with translating nature language questions into data from analysis. A typical search can be tripped up with the choice of words used by an individual and may get the individual user incorrect results to their search query. This can make search for the correct information on search engine especially difficult to those who do not have the background in library and/or information sciences.
A real language (as opposed to a search language) method of finding information on a search engine would be extremely handy and would advance how the Internet could be used. This would make WolframAlpha a “computational knowledge engine” for the Web. Because of its ability to go beyond the simple regurgitation of documents that contains parts of the answer. If Wolfram Alpha can actually compute the answer to a posed question in the time it takes a user to scan through the other open frames on their web browser, WolframAlpha could redefine how we interact with the Internet.
If we are to believe that the web is a conversation from one-to-few or one-to-some, then the design and organization prevents an interactive conversation between the two parties. Web artifacts are framed in a context in a similar nature to the traditional publishing of a book or a magazine. The difference is merely the addition of other forms of media (audio, video, animation). To create a conversation, one must have (surprising enough) two parties communicating with each other. Since WolframAlpha should have the ability to answer certain kinds of questions in a form that is close to natural communication, it could be the starting point to the "Web as Conversation."
It is important to note that this is not the first attempt at such a service. Cuil was designed based on the same principle early and really was considered broken as it could not handle the strain of a large group of individuals using the site at the same time. If WolframAlpha can support being Dugg or SlashDotted or even an onslaught by the Twit Army and can maintain the same level of service, it will be huge.