Looks like things have been mostly answered thus far. Dual core is very similar to hhaving dual processors.

The big advantage companies are seeing though is they can nearly double the processing power per inch in their racks. For example, the Proliant DL585 server takes 4 AMD processors. Putting dual core chips into it results in pretty much an 8 processor box, but with the price being slightly higher then the non dual core version, instead of much higher going to 8 real processors.

Consumers aren't going to see a ton of advantage until more programs switch to multithreading. It's very much a chicken and egg situation, but with the hardware coming out now, the programmers will finally see reasons to do it. For now, clock speed has hit a brick wall for the most part, so dual core makes a lot of sense.

I'm just waiting/hoping for a dual core Powerbook. OS X is very capable of taking advantage of dual processors, so it would give a noticible speed boost to a laptop line that hasn't seen equal growth to the x86 world in the past two years.