The short and sweet answer...
Every CPU has registers, and logic.
A register has an input and an output. The output is held until it sees the rising edge of a clock, then it copies the input to the output.
Logic simple has a lot of inputs, and a lot of outputs. The outputs depend only upon the inputs, and it takes a certain amount of time for the inputs to cause a change in the outputs. Note that this time depends on the process and materials used in making the part, the complexity of that particular section of logic, temperature, and voltage.
A clock pulse hits, and all registers latch their data. Then, the outputs of the registers have to go through the logic and make it to the inputs of the next set of registers before the next clock pulse. So, in a real sense, it is mostly the speed of the logic that determines the maximum speed of the part. (there is some delay associated with the registers too, but we will assume that this is not the case to simplify the analysis)
So, let's assume that the data has to go through X amount of logic in order to be processed. Let's also assume Intel splits the logic into 20 pieces, with 21 sets of registers. So, the maximum clock speed is the time in which X/20 can be done. This is called pipelining. if you have a 20 stage pipeline, then each section of the pipe can process one instruction at a time. This means that there are 20 different instructions all in various stages of completion.
Now, let's assume that AMD only splits the X into 10 pieces, so their maximum clock speed is X/10. So their clock speed on average is half that of Intel.
This is the extremely simple guide to why one company has lower clock speeds. But you also need to keep in mind that this is not the whole picture when it comes to performance. Intel has a deeper pipline, but more work must be "thrown out" in the event of a branch mis-prediction. So, just increasing the pipeline depth brings diminishing levels of return. I suspect that Intel is already at the point where increasing the pipline depth would not help at all.
So, the extra-short anser is that AMD has slower clock cycles, but they do more in each cycle to make up for it.