There are two issues here, firstly dual core concept, and then pentium V core duo.
If you dont mind.. lets split this into two questions..
Single core V dual core.
As your familiar with a 2.66Ghz Pentium IV, lets compare with a Dual Core Pentium D running at 2.66Ghz. Program design can either be threaded (which means the program is divided up into several 'micro programs', or a single process. A single process application cannot make use of multiple processors, so it will perform almost exactly the same on a dual core, as it would on a single core processor. I say almost, because windows itself has a small overhead, and any background tasks you run at the same time will benifit from having a spare processor.
Of course if you run several single process applications (multi tasking), then the second core will be used considerably more. It still wont be like having a 5.32Ghz processor.. The applications wont complete in half the time, but it will mean the system can run more applications than a single core computer before it slows down.
Finaly there is the holy grail of multi processor goodness, the multithreaded application. Programs written like this break down into several mini programs, each of these mini programs can be run on separate cores, only pausing when data from one thread is required in a separate thread. Typically performance benifits in a well written multithreaded application can be anywhere between 50% and 95%. ( A web server application for example could use 1 thread for each user request, so if 100 people are browsing, 100 theads could be spread across 100 cores and be extremely efficient). This is the only time that a multicore processor will actually be able to complete a single program faster than a single core chip. (Edit.. I dont mean webserver is the only example.. I mean multithreaded applications are the only time that dual cores can complete single applications considerably faster)
Ok, So thats Single V Dual (Feel free to ask more questions

) so now Pentium IV compared to Core 2 Duo (Core Duo was replaced very fast so I will focus on the superior Core 2 Duo).
Pentium IV's can theoretically process 2 Integer instructions, and 1 Floating point (or MMX/SSE) instruction at the same time, this is called a 'three issue core' as it can do 3 tasks at the same time. Not only this Pentium IV runs its integer instructions at Clockspeed X 2. So in theory its a very powerfull processor for integer applications. Unfortunatly due to several design issues, its rare that the P4 doesnt just run out of data. It then sits there doing nothing waiting for new instruction to process. It was very fussy about program design, and running programs optimized for older Pentium III processors makes the P4 look even slower. In reality P4's generally seem to average 1.5 to 2 instructions on each clock tick. (Available as single core, or Dual core Pentium D)
Moving briefly to AMD's Athlon 64, its also a 3 issue core, however its a much better design, and is an excellent processor for running applications optimized for Pentium III. Infact even fairly badly optimized code will not slow this AMD chip considerable. A very good design. This chip averages 2-3 instructions per clock tick. (Available as Athlon64, or dual core X2's)
Finaly Core 2 Duo. Each core of a Core 2 Duo is able to process 4 instructions at the same time, and in very rare instances its even able to combine 2 instructions into one before its send to the execution units in the processor, this simulates running 5 instructions at once. That said, the combining is a 'new thing' and Core 2 Duo struggles to do this on 64bit code, so it only really happens with 32bit software. Like the AMD Athlon 64, Core 2 Duo is much better at handling less perfect applications, this chip will average 3-4 instructions every clock cycle.
So in very simplistic terms, at 2Ghz, the Core 2 Duo is processing as many instructions (on a single core), as a Pentium IV (or Pentium D) would process at 4Ghz, because Core 2 duo is twice as efficient. AMD 64 sits somewhere between the two, depending on the application the AMD will be between 10% and 40% slower than the Core 2 Duo.
Its not quite as 'simple' as this.. but in basic terms thats the differences between Pentium and Core 2 Duo... So in the future, when you see people with dual core 2.66Ghz computers claiming they have 5.32Ghz computers you will be able to laugh. Just think about cars... If you have 1 car that can carry 4 people 70 miles in 1 hour, and then you buy a second identical car, you still take 1 hour to travel 70 miles, but now you can carry 8 people. Dual core doesnt mean you can do work faster, but you can do more work at the same time, if and when the programs allow it.