In regards to a multi-core processor: Is a triple core processor (for example) essentially like having 3 processors of a given clock speed (in my case, 3.2 GHz), or is it more like splitting a workload between 3 people (as an analogy), thus taking only a third of the time/effort? This is something I've never been able to find out for sure.
It is both as you described. Three cores are similar to having three processors, and the three cores will share the load and get things done faster.
Now as far as applications being able to take advantage of the cores so that the work can be split between them that depends on the application.
Most new applications, games, phot software, video software can take advantage of all the cores and when they do yes indeed things get done much faster.
For simple things like web browsing and such you won't see much of difference. When you start to open many applications the difference is noticeable as threads and processes can be handled and split among the cores just like a few people can do more things at once then one person can..
Bruce said it pretty well. For an application that only utilizes one thread(core/processor), a higher clock speed(Ghz) processor will do it quicker, but when/if said app can utilize all the cores(multiple processors), the same project/task will be done much quicker, even if the cores run at a lower clock speed.