But first a little info on the clock hardware.
The principle of crystal oscillation is behind most computer clocks. A properly cut quartz crystal which is mounted under tension can be made to generate a periodic signal of very high accuracy. The frequency of the oscillation depends upon the type of crystal and the tension it is subjected to. This signal is used as the synchronizing signal to every circuit in the computer. Think of the clock as the conductor of an orchestra and the rest of the computer components as the musicians who play the symphony. Another way to look at the clock is as a traffic cop who controls the flow of traffic by periodically stopping some and letting others move.
The signal from the oscillator is fed into a counter to make it count down to zero. When the counter gets to zero, it causes a CPU interrupt, resets itself to its max value and the cycle continues. The max value is saved in a holding register from where it can be copied into the counter.
The periodic interrupts from the clock hardware are called clock-ticks. Modern computers have programmable clocks in which the interrupt frequency can be controlled by software.
The CPU can respond to the clock interrupt in a variety of ways, one of which is the initiation of a context switch.
One more thing. The clock task is designed in such a way that it is guaranteed to finish its work before the next clock tick arrives.