For a digital clock that runs with an line operated supply, you can arrange to use part of the AC waveform to produce a 60 Hz waveform. If you apply that signal to a counter, one second will have elapsed every time the count reaches 60.
A 60 Hz waveform goes through 60 repetitions in one second. An 8 MHz waveform goes through 8,000,000 repetitions in one second. Frequency is always cycles (or repetitions) per second.