Alpha allows users to create a personalized search engine homepage using an a simple drag-n-drop interface. One of the main differentiators seems to be that unlike Google CSE (which is closely tied to Google Web Search) Yahoo! Alpha shows search results from various Yahoo! properties and third-party services on the same page (Flickr, YouTube, Wikipedia and your own if you can provide search results via RSS feeds).
There's also a special module called "Sponsored Results" that displays text ads based on your search query. This gives a strong hint that Yahoo! may be planning to share ad revenue with users just like Google's CSE.
Title of this post came from Pete Cashmore's keen observation about the naming:
Yahoo launched a service today called Yahoo Alpha (beta) - an ironic name that may be taking a potshot at rival Google’s tendency to put everything in beta.