DIN sync, also known as sync 24 or sync 48, is a simple way to get step sequencers, such as the ones in drum machines and some synthesisers, to tell each other when to start and stop playing, and what tempo to play at.
It consists of two different signals, each on a separate wire: the clock pulse signal (which is like a steady stream of triggers); and the run/stop signal (which is like a gate). Depending on the manufacturer, a certain number of electronic pulses is sent for every crotchet, otherwise known as a quarter note. Roland used 24 pulses per quarter note; Korg used 48; and Oberheim used 96. Almost no one uses any of these anymore, as MIDI has made DIN sync in general obsolete, but let's ignore that for the time being.
It looks like DIN sync doesn't represent the clock so much as it is the clock. It doesn't appear to synchronise the slave's clock with the master's clock, so much as it seems to bypass the slave's clock entirely, directly plugging the master's clock into the slave's sequencer via some wires. With that in mind, it gives us a glimpse into how these machines might be working internally, using their own clock to talk to their own sequencer.
Let's imagine a Roland compatible sequencer, for example. Its clock sends out a steady stream of pulses, and the sequencer counts them, using each batch of 24 pulses to measure a quarter note. In other words, it counts 6 pulses per sixteenth note, as might be more useful to measure, as most step sequencers deal exclusively with sixteenth notes. The clock is unwavering in its pulse sending task and doesn't care whether anything's paying attention to it or not.
Then when the musician tells the machine to start playing, the run/stop signal goes high, the sequencer politely waits until the beginning of the next clock pulse, and then it finally starts playing notes. In the case of the afforementioned step sequencers, this simply involves waiting until six more pulses have been counted and then incrementing the row, triggering off envelope generators or updating the pitches of oscillators as required.
As with the UNIX philosophy, this indicates that under the hood, machines such as drum machines and some synthesisers — anything with a built-in sequencer — contain several discrete parts talking to one another, including a clock sending out pulses at regular intervals, and a sequencer counting those pulses and updating its outputs accordingly. The sequencer itself isn't aware of the time at all. It's not doing anything as complex as counting the milliseconds between the pulses. It's simply counting the pulses themselves, no matter how fast or slow they come.