Android's sharing capability, known to developers as a form of "intent," is about more than merely sharing in the social-oriented sense of the word. It's a way for you to quickly and easily pass data between applications -- anything from a Web page to a chunk of text or even an image.
The most important part about Android's sharing system? Any application can take advantage of it; all a developer has to do is declare his program capable of receiving data, and boom: It'll show up throughout the OS as a place to which data can be shared. That's a sharp contrast to the setup on certain other (ahem) more restrictive mobile platforms, and the resulting difference in usability is enormous.