Palladium was the old name for what is now known as "Next Generation Secure Computing Base".
Basicially, it's a feature of the coming windows, codenamed Longhorn, that will add a 'trusted mode' to the operating system.
Said trusted mode will protect data from the untrusted mode, and it uses some hardware support for storing keys, namely the TPM, a little chip on your motherboard. This will effectivly tie the keys to one computer (although all but two keyswill be transferable).
It will not hinder the executing of not-trusted code, but it will prevent data exchange from the untrusted to the trusted mode. (The other way around is *not* a security risk, but if that's prohibited as well, you'll know for a fact that it is an anti-piracy measure).
The original Palladium (the one with all the bad reputation) actually went much further than this, but it seems Microsoft has deemed it unworkable (which it was).
Chances are it won't stop piracy, as it can't really fight hardware hacking, but it might make Windows much more secure.
In the worst case, you'll always be able to turn it off and work as you did before.
The Nexi actually are modular and exchangable... so there might be a nexus that allowed you to store all keys on a smartcard, for example. But I heard, only one Nexus will be able to run at one time.
-- Tyberius Prime
Ps: The following the original text of this faq. Make sure you understand the technicalities behind it before you get infected by the 'Palladium is all evil' meme.
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It is a Microsoft initiative which combines chips and motherboards with their next operating system in an attempt to stop piracy. It has a lot of people worried as it will ultimately lead to MicroSoft taking over the world (allegedly). See the resources below: