I don't know the juicy details on each, but i can at least kind of give the basics.
Pentium D is a single-core processor
Pentium Dual Core is a Dual (2) core processor.
Basically, the more processors you have the better (generally)
So the Pentium Dual Core is better than the Pentium D.
I don't know exactly how it all works but the dual core is able to multi-task better since it can have 2 strings/threads going, giving less of a load on your processor when running multiple or high demanding programs.
Duo 2 Core is pretty much standard now.
LOL cancel what i said, i just read the Pentium D and its a dual core too. Sorry. I should research first, owned myself :]
After a quick browse, looks like the Duo Core is newer technology than the Pentium-D. The Duo Core is able to dish out more stuff with lower wattages and mhz than the Pentium-D.