Let me explain this in short and easy way , :
Clock speed is the measurement of a computer part in terms of frequency , just like what a speedometer does in a car in terms of Km/h.
It provides a reference to measure the speed at which parts like processor (CPU,GPU) and memory modules work.Higher the clock rate , higher the performance will be.
Yes , Its true that Higher the clock speed , faster the CPU. However in modern day CPUs many other factors also affect the performance which can not be decided based on CLock speed only.
SOme of these factors are : CPU Cache memory ,N

f Cores, CPU Architecture and no. of transistors , CPU Thermal design , Memory Controllers , Hybrid modes Turbo Boost , etc.
CPU Cache Memory is the amount of nearest memory available to the processor to store temporary information.(Exclude Registers)
Its much faster than RAM and very small in size ,(from 32kb to 12mb generally).
Cache has various levels as well , like L1,L2,L3.
No. Of Cores : # of physical cores determine the number of processes a CPU can handle at once. More the number of Cores , the more number of processes a CPU can execute at once.
Modern day processors include : Bulldozer/FX series Proccy from AMD , having upto 16 Cores.
Turbo Boost : Intel CPU's like COre I5,Core I7's feature Turbo Boost , which can disable rest of the cores and divert the power to primary or main cores , to boost the operation for single thread application.[It actually boost the frequency of the cores, i.e. clock speed]
Design : YOu will notice that day by day processors are getting smaller and smaller in size , but they include more and more number of transistors in the die. [VLSI,ULSI,etc] are the factors that determine the no. of transistors present in a CPU.
Also modern CPUs come along with various design for the way these transistors are placed together.Intel Ivory bridges feature a 3Dimensional TRI design.
THe presence of memory controllers, inbuilt Graphics processor on the CPU die , etc affect the overall performance upto a large extent.