Nineteen is the number of years for the moon's phase to again be in phase with the same time of (solar) year. This is a continuous phenomenon, linking any moment with those future and past times nineteen years apart, or multiples thereof. The simple measure of this period is 235 lunar months, which is 5 times 47 lunar months, Octon eclipse periods.
The definitive Saros cycle of eclipses (used today) is 19 eclipse years long.
The effect of 19 is found in the metrology of measures associated with lunar counting since the solar year is 12 plus 7/19 (or 12.368) lunar months long. The lunar orbits in a solar year must be exactly one more than lunar months, then they number 13 plus 7/19 (or 13.368) lunar orbits in a solar year.