How Does DUO Core Work ?

It doesn't mean double the rated speed, no.  What it means to have a multi-core processor, is that it's essentially the same as having multiple processors inside your PC.  The difference is important here, between having multiple processors who's total speed adds up to 3.2ghz, and having one single processor that is running at 3.2ghz.  If an application is programmed to be capable of "multi-threading" (in short, taking advantage of multiple CPU cores at the same time), then it will be much more efficient running such a programme on a multi-core CPU than it would be on a single-core CPU - this is because the programme is working on two different aspects of the programme at the same time, as opposed to a faster single-core CPU which would only be able to handle one aspect of the programme at a time.  Because of the limitations of other parts of your system, and because of (in certain circumstances) the laws of physics themselves, it becomes much more efficient to have a job being carried out (or a programme being run) by two lower-speed CPUs at the same time, rather than one CPU running at twice the speed.

This being said, if a programme is *not* written specifically to take advantage of multi-core systems, then running it on a system that has two 1.66ghz cores vs one system with a 3.2ghz core would not, nesc, be an advantage - since only one of your cores would be doing any work, whilst the other sat idle, and this single core is only applying 1.66ghz of CPU "grunt" to the task in hand.  However, if this is the case, dual-core is *still* not out of tricks.  Because Windows (XP and Vista) support multi-core CPUs in their current iterations, it is wholly possible that you could use your computer to perform two reasonably system intensive tasks at the same time, if you have a multi-core CPU, as one of the cores could be dealing with one task, whereas the other core could be dealing with the other.  It might seem like a standard single-core CPU is, in fact, capable of just this (as the advent of the ability of CPUs and OSS to provide us with "multi-tasking" would suggest), it is in fact not - if you have two system intensive tasks being carried out on your single-core system, they are in fact taking it in turns to use the Cpu grunt - so, they're only getting your 3.2ghz CPU for half the time that they would get your 1.6ghz core in a dual-core CPU - thus, it is in no way more efficient, since having a 3.2ghz CPU for half the time of a 1.6ghz CPU equates to the same as just having a 1.6ghz CPU anyway (it's a little more complicated than this, and I could get into talking about various things like on-die cache that make dual-core CPUs more efficient, but I think that's moving away from the point a bit).

So, in short, the answer to your question is "it depends what sort of work you are carrying out with the computer, how you are using it, and if the applications were written to take advantage of multi-core hardware".

Oh, and don't expect many software programmers to make the change from single-core to dual-core when writing their software any time soon - the main reasons being that anything written exclusively for dual-core will not work on single-core (whereas anything written for single-core will still work fine on dual-core), and the market take-up stats suggest that multi-core, whilst fast becoming the standard, does not hold a lion's share of the market yet; also, the facts are that writing a threaded application is a lot harder than writing one for a single-core.

1.66 GHZ system means that your system processor now will work as 3.22GHZ. The processing tasks will be divided among the cores. You can think this core as brain, so dual cores mean dual brains. For more information about duo core, visit the following link.
Duo Core