The tun is the unit by which Classic Maya public time was actually measured out, because it is the period at which rulers commissioned monuments. Stelae were raised to mark the completion of a tun, more often a half-katun of ten tuns, and most often a katun of twenty, and the resulting series of dated stones is the backbone of Classic chronology.
That habit has a consequence historians rely on. A site with a long uninterrupted run of period-ending monuments is a site with a functioning court through that span, and the point at which the series stops is evidence about the end of that court, which is how the ninth-century collapse of the southern lowland cities is dated site by site. The last dated monument at a given city is a real datum rather than a gap in the record.
The tun is also where the count leaves strict base twenty. Eighteen winals make a tun, giving 360 days rather than 400, which brings the unit within five days of the solar year without ever being corrected to match it. Above the tun the multiplication by twenty resumes and is not broken again.
There is a second reason the tun matters to historians. Because the Long Count is linear, two dated monuments anywhere in the Maya area can be placed in order and the interval between them stated exactly in days, without any assumption about correlation with the European calendar. That property is independent of the correlation debate: even if every Maya date were shifted by some constant, their relative order and spacing would be unchanged.