As far as Wikipedia seems to say (since NOTHING else I'd check actually tells me what it's doing. They conveniently stopped updating for this month, just as the big risk they've been mentioning finally was unleashed.), The new version (which everyone connected to the internet and having any version of Conficker now has or is now downloading) does not spread (which sounds really stupid to me). It downloads from 500 sites from a random list of 50,000 with over 110 TLDs (.com, .org, .edu, etc) (I don't know what it's downloading), kills all anti-malware processes it detects once a second, disables auto-update, and prevents you from opening websites related to anti-malware or auto-update.
And then there's the odd part, the new thing that people really don't understand yet: It creates a peer-to-peer network and shares some data with other Conficker "enhanced" computers. People aren't sure what it's doing with that, but that's the big interesting thing none of the others have been doing. So, that is, from what I can tell, basically the point of this entire virus: sharing... something.