Why are clocks used in computers?
Clocks are used in computers for the simple reason that most if not all of the circuity is synchronous sequential logic.


  In a synchronous circuit, an electronic oscillator called a clock
  generates a sequence of repetitive pulses called the clock signal
  which is distributed to all the memory elements in the circuit.


Now, that may not seem satisfying and granted, you would reasonably ask "why are synchronous circuits used in computers?" but that's an easy question to answer too:


  The main advantage of synchronous logic is its simplicity. The logic
  gates which perform the operations on the data require a finite amount
  of time to respond to changes to their inputs. This is called
  propagation delay. The interval between clock pulses must be long
  enough so that all the logic gates have time to respond to the changes
  and their outputs "settle" to stable logic values, before the next
  clock pulse occurs. As long as this condition is met (ignoring certain
  other details) the circuit is guaranteed to be stable and reliable.
  This determines the maximum operating speed of a synchronous circuit.


An active area of research is asynchronous computing where most if not all of the circuitry is asynchronous sequential logic.