It is fairly simple. You need to ensure that everyone knows to stop! Communications weren't instant, so both sides needed time to get the word through the front to avoid the awkward situation of one side laying down their arms upon hearing the news and the other, ignorant of the development, still shooting them. For an Armistice to work effectively, everyone needs to know there is an armistice. The practical result of this, of course, varied. Some units upon receiving word, were happy to hunker down and do their absolute damndest to survive a few more hours. Others though continued to fight until the last minute, mainly at the behest of officers obsessed with one last opportunity for honor and glory before the fighting ended, such as was the case with the Italian-Austrian front, where the delay from signing to implementation was a full 24 hours, allowing for a rather sizable last push by the already victorious Italians that the Austrians has no interest in actually trying to stop. The long delay seems to have been purposeful on the part of the Italian officers leading the negotiations, who were eager to avenge the earlier defeats that they had suffered. The Italians weren't the only unit on that front eager to prove their mettle in the last moments of the war though, as apparently a small American contingent had only just arrived on the front, and wanted to ensure that they didn't miss out on the experience of combat due to their poor timing and "unsoldierly passivity on the part of the enemy" as one observer noted.

In some cases there were at least theoretical military concerns at play. On the Western Front, a British brigade was ordered at 9:30 that they had an hour and a half, maximum, to seize a key bridge over the Dendre River, as there were concerns that the Germans might blow it up. No one knew if the Armistice would hold or not, so many commanders maintained an eye on what might serve them well if hostilities resumed. The bridge was taken with time to spare.

Regardless though, for both the gung-ho and the "just a few minutes more", when the clock struck the hour, the front went quiet.

The First World War: Germany and Austria-Hungary 1914-1918 by Herwig

The First World War by Gilbert