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.