The clock rate is the rate in cycles per second (measured in hertz) for the frequency of the clock in any synchronous circuit, such as a central processing unit (CPU). For example, a crystal oscillator frequency reference typically is synonymous with a fixed sinusoidal waveform, a clock rate is that frequency reference translated by electronic circuitry (AD Converter) into a corresponding square wave pulse [typically] for digital electronics applications. In this context the use of the word, speed (physical movement), should not be confused with frequency or its corresponding clock rate. Thus, the term "clock speed" is a misnomer.
A single clock cycle (typically shorter than a nanosecond in modern non-embedded microprocessors) toggles between a logical zero and a logical one state. Historically, the logical zero state of a clock cycle persists longer than a logical one state due to thermal and electrical specification constraints.
CPU manufacturers typically charge premium prices for CPUs that operate at higher clock rates. For a given CPU, the clock rates are determined at the end of the manufacturing process through actual testing of each CPU. CPUs that are tested as complying with a given set of standards may be labeled with a higher clock rate, e.g., 1.50 GHz, while those that fail the standards of the higher clock rate yet pass the standards of a lesser clock rate may be labeled with the lesser clock rate, e.g., 1.33 GHz, and sold at a relatively lower price. 
The clock rate of a CPU is normally determined by the frequency of an oscillator crystal. The first commercial PC, the Altair 8800 (by MITS), used an Intel 8080 CPU with a clock rate of 2 MHz (2 million cycles/second). The original IBM PC (c. 1981) had a clock rate of 4.77 MHz (4,772,727 cycles/second). In 1995, Intel's Pentium chip ran at 100 MHz (100 million cycles/second), and in 2002, an Intel Pentium 4 model was introduced as the first CPU with a clock rate of 3 GHz (three billion cycles/second corresponding to ~3.3 10−10seconds per cycle).
With any particular CPU, replacing the crystal with another crystal that oscillates half the frequency ("underclocking") will generally make the CPU run at half the performance. It will also make the CPU produce roughly half as much waste heat. Conversely, some people try to increase performance of a CPU by replacing the oscillator crystal with a higher frequency crystal ("overclocking"). However, the amount of overclocking is limited by the time for the CPU to settle after each pulse, and by the extra heat created.
After each clock pulse, the signal lines inside the CPU need time to settle to their new state. That is, every signal line must finish transitioning from 0 to 1, or from 1 to 0. If the next clock pulse comes before that, the results will be incorrect. Chip manufacturers publish a "maximum clock rate" specification, and they test chips before selling them to make sure they meet that specification, even when executing the most complicated instructions with the data patterns that take the longest to settle (testing at the temperature and voltage that runs the lowest performance).
Also, some energy is wasted as heat (mostly inside the driving transistors) whenever a signal line makes a transition from the 0 to the 1 state or vice versa. When executing complicated instructions that cause many transitions, higher clock rates produce more heat. If electricity is converted to heat faster than a particular computer cooling system can cool it, then the transistors may get hot enough to be destroyed.
Engineers continue to find new ways to design CPUs that settle a little quicker or use slightly less energy per transition, pushing back those limits, producing new CPUs that can run at slightly higher clock rates. The ultimate limits to energy per transition are explored in reversible computing, although no reversible computers have yet been implemented.
Engineers also continue to find new ways to design CPUs so that, although they may run at the same or a lower clock rate as older CPUs, they get more instructions completed per clock cycle.
The clock rate of a CPU is only useful for providing comparisons between CPUs in the same family. An IBM PC with an Intel 80486 CPU running at 50 MHz will be about twice as fast as one with the same CPU and memory running at 25 MHz, while the same will not be true for MIPS R4000 running at the same clock rate as the two are different processors that implement different architectures and microarchitectures. Furthermore, there are many other factors to consider when comparing the performance of CPUs, like the clock rate and width of the CPU's data bus, the latency of the memory, and the cache architecture.
Clock rates should not be used when comparing different CPUs families. Rather, software benchmarks should be used. Clock rates can be very misleading since the amount of work different CPUs can do in one cycle varies. For example, superscalar processors can execute more than one instruction per cycle (on average), yet it is not uncommon for them to do "less" in a clock cycle. In addition, subscalar CPUs or use of parallelism can also affect the performance of the computer regardless of clock rate.
In the early 1990s, most computer companies advertised their computers' performance chiefly by referring to their CPUs' clock rates. This led to various marketing games, such as Apple Computer's decision to create and market the Power Macintosh 8100 with a clock rate of 110 MHz so that Apple could advertise that its computer had the fastest clock rate available—the fastest Intel processor available at the time ran at 100 MHz. This superiority in clock rate, however, was meaningless since the PowerPC 601 and Pentium implemented different instruction set architectures and had different microarchitectures.
After 2000, Intel's competitor, Advanced Micro Devices, started using model numbers instead of clock rates to market its CPUs because of the lower CPU clocks when compared to Intel. Continuing this trend it attempted to dispel the "megahertz myth" which it claimed did not tell the whole story of the power of its CPUs. In 2004, Intel announced it would do the same, probably because of consumer confusion over its Pentium M mobile CPU, which reportedly ran at about half the clock rate of the roughly equivalent Pentium 4 CPU. As of 2007, performance improvements have continued to come through innovations in pipelining, instruction sets, and the development of multi-core processors, rather than clock rate increases (which have been constrained by CPU power dissipation issues).