Even for us hardcore techies here at Unplggd, there remains many questions about what makes a particular computer faster. In the late 1990s and early 2000s, all the rage for computers was to have one with higher clockspeed. The death of the Pentium 4 saw that fad slowly die. Yet, the megahertz arms race still confuses consumers and techies alike.
Computer processors are complex beasts that to most are merely black boxes. Their design changes and costs do not resonate with most consumers as we are not die engineers. This is why Intel and other chip companies focus their advertising to convince consumers that the next generation is better and faster, often with things like higher clock speed to "quantitatively" show progress.
Clockspeed for computer processors is merely a function of how many times per second a processor can compute an instruction. If two processors have the same architecture (basic design), the one that has a higher clockspeed is faster at executing code run though it. Where the confusing arises is if two processors have different architectures then the clockspeed means very little. For example, a 3.8 GHz Pentium 4 is very slow compared to a top of the line 3.8 GHz Core i7. This all stems from how processors actually work with the instructions they process.
Processors have what are called "pipelines". And like the name implies, these "pipes" are where data travels through in the processor as it enters and leaves. Older processors had larger and or less efficient pipelines, meaning that they could not move as much information, thus slower performance. Modern processor pipelines are shorter or have better features which allow them to not only move through information in fewer stages, but also ensure that it can make fewer errors. Those factors can combine meaning that modern processors get significantly more work done in each cycle making a processor with a lower given speed actually perform operations much faster.
For more information check our Ars Technica article.
(Top image: flickr member Justin Ruckman, second image: flickr member Guillo75, both licensed under Creative Commons)

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Part of the problem with the Pentium 4 architecture was that it had the longest data pipeline of any CPU at the time. Intel's development of hyperthreading split that long pipeline in half, giving the P4 the ability to run 2 separate threads per clock cycle. For all intents and purposes, this doubled the effective number of CPUs available.
This is why, when you look at Task Manager on your new 6-core i7 CPU, you see 12 "processors". The absolute pipeline in each core probably isn't any shorter than what the P4 had, but again because of hyperthreading technology, each core runs like 2.
Possibly interesting side note: a 1.8 GHz Pentium M processor in a laptop would run just as well as a P4 in the 3.2-3.4GHz range. This was because the P-M was based on the P3 CPU, which had a much shorter pipeline than the P4, and that allowed a much slower CPU to keep pace very well against the numerically-faster desktop CPU. Add in some of the multimedia enhancements first developed for the P4, and it's no wonder the P-M was still good even through the P4's last gasp, the true dual-core Pentium D.