This might take awhile to explain, so before you read further, grab a cup of coffee.
"Dual Processors" means that one a single processor chip (known as a "die"), there are 2 cores. Like on cars, there are V4, V6, and V8. V4 means 4 pistons, V6 means 6, and so forth. Dual processors means you have two processor cores working for you, but on one SINGLE chip. So before there used to be single core Pentiums. A orthodox use "dual" would mean two Pentium processor chips on the same motherboard. But Intel combined two Pentiums into one SINGLE chip instead of two separate chips, for faster communication between each core.
Quad means the same thing. Instead of having 4 individual processor chips soldered in 4 different places on the motherboard, there is one SINGLE chip with all 4 cores smashed in there.
You can't calculate computing power in linear terms. It's more ... logarithmic. And each generation (Pentium 1, 2, 3, 4 and finally the Core series) has a different architecture. Like houses from the early 1900s, and early 2000s. Suppose both houses have the same sq. footage, but different arrangement of rooms, size of rooms, ceiling height, etc. Pentiums had different arrangements of its components than a Core Duo chip. Newer architecture usually can outperform an older, higher clock speed (GHz or MHz) at a lower clock speed.
An Intel Core Duo running at 1.8GHz can benchmark better than a 3GHz Pentium 4 due to faster, better, and newer architecture.
Now dukebound85 mentioned "multithreaded apps". Each application had a single "thread" since processors at that time was only single core. Multithreaded allowed applications to have multiple threads. Think of this like instant messaging windows. Suppose you are iming 5 people. A single core processor would have to handle those one by one, shutting down each window as it cycles through the 5 windows. But, with multi threading, it was able to handle multiple windows at once.
