What astronomical event corresponds to the passage of one month?

The moon revolves around the earth once, and we observe the cycle from new moon to full moon.

That lunar cycle takes approximately 29 1/2 days.  So if we were still to follow a lunar calendar, we'd lose about 11 days per year compared to the Gregorian calendar which we follow.  The Gregorian calendar is named after Pope Gregory XIII, who introduced the calendar in 1582 as a reform to the Julian calendar (named after Julius Caesar), which had been followed since Roman times.  

A historical item of interest about the Gregorian calendar:  Because Russia was dominated by the Orthodox Church and opposed to anything a pope had introduced, Russia continued to use the Julian calendar until 1918, after the communist revolution changed the governing authority in Russia.