Furthermore, how would a sound sleeper not accidentally oversleep an important meeting?
There are many questions in the Q&A section that touch the subject of waking up before the time of alarm clocks. People who were important enough to attend "important meetings" likely had servants to wake them up or to relay the message, as minnabruna point out in a previous thread. This is the extent of my knowledge on the matter, and like those servants, I am merely relaying information!
In pre-Christian northern Europe, people used "daymarks" as a unit to measure time - I believe the Catholic canonical hours (Vespers, Prime, Terce, etc.) were descended from that. I don't have a specific source for the relationship, but both are ways of dividing days into roughly three-hour chunks, or about a quarter of the daylight hours* (or an eighth of a whole 24-hour period). Noon is halfway, two quarters before, two quarters after.
Here's a Harvard page on daymarks that also mentions a few other pre-clock ways of dividing a day.
As said earlier, our modern system of time-keeping divides each sun-cycle into twenty-four hours, each of which is 60 minutes long. The Scandinavians divided each sun-cycle (sólarhringr, "sun-ring" in their language) into eight sections. They did this by dividing the horizon into eight sections (north, northeast, east, southeast, south, southwest, west, and northwest). Each of these sections was called an eighth (átt or eykt). A place on the horizon which lay dead center in any of these eight directions (due north, due northeast, etc.) was called a daymark (dagmark). The identified the time by noting when the Sun stood over one of these daymark-points on the horizon.
(* near the equinox, up north - the relation to noon is always the same, no matter when sunrise takes place.)