This section begins with a statement that a game cannot be properly run if a DM does not keep strict track of the passage of every last second of game time. It goes on to explain why, and makes some convincing arguments, but in the style of play that arose in the "second generation" which we have discussed, I'm not sure it's quite as vital as Gygax insists. Few--if any--DMs I have ever known kept strict track of the passage of minutes, hours, days, weeks, months, and years, preferring instead to "wing" the passage of time, figuring things occur "over about the course of a week," or "Take about half a day."
But Gygax is working under a different assumption. The book seems to operate under the idea that gaming--for the DM, at least--is a more all-encompassing hobby than pretty much any other, that a DM will be constantly running games in his world, with three to five different groups, and sometimes single players attempting to catch up in levels to one or more parties, or fulfilling a personal quest. And for the multiple adventuring scenarios he lays out, I can see where time in the campaign world would require strict record keeping (and honestly, I kind of wish I had the time, energy, and creativity to run a game like that; it could be a lot of fun).
Time in the Dungeon: This section, a mere two paragraphs, gives a few tips on keeping track of how long passes between events underground or on an exploratory adventure. It reminds the reader of the one-minute round, ten-round Turn, and six-turn hour breakdown, and generally allows for players to "hole up" overnight or over a period of several days, which does not excuse them from wandering monster checks but advises that such checks be mitigated based on precautions taken by the PCs.