This circuit uses 60hz AC as a clock pulse source for running a digital clock. 60hz AC is used to produce a 60hz clock signal, used to advance a second counter once every 60 pulses (one second).
When the second counter reached 60, it resets, advancing the minute timer. Likewise, the minute counter advances the hour counter, a 24 hour clock, every hour.
Human-readable display of the current time would require a binary to BCD converter which, unfortunately, won't fit on this circuit. However, see http://everycircuit.com/circuit/4799369760210944 for a suitable display.
