A great feature is that if one of the lines on your map is 'broken' in some way (indicated by a red x), you can simply double-click on it, and Windows will troubleshoot the problem, and offer a range of solutions, all of which can be implemented with a single click of a button, very clever.
A computer connected to the internet via a LAN:
A network with a broken link:
From this Center, I can view the status of my primary connection (the LAN, in this case). Underneath this is 'Sharing and discovery', which provides a simple set of options allowing for the sharing of files/printers/media, and also contains the options for Network Discovery.
File sharing works pretty much the same as it did on XP, with the 'Public' folder replacing 'Shared documents' as a way for multiple users on the same computer to have a common folder to share documents. Sharing across a network works in much the same way, except that in the 'properties' window of a folder, you can specify *exactly* who that folder is shared with, rather than just having it set to shared, or not.
The Network Discovery feature is one that I'm not entirely sure about, but can easily be simply set to 'on' and then ignored. And, if you find a reason to turn it off or customise it, the options are all readily available for you to do so. The features affects whether or not you can see (and be seen by) other computers and devices on your network, and whether or not you can access shared devices and files on the network, and vice versa. Given that Vista now allows you to specify what sort of network (public, work, home) you're on, it may be useful to have this as 'on' or 'off' for a certain type of network - but mostly, whenever I connect to a network, it's for the purpose of using the network resources, so I can't see a situation where I'd turn this one off.