"Yom" means day. It is one of those Hebrew words that cannot be reduced beyond itself. Its very root means day, the measure of time that governs our activities in the cycle of light and darkness.
We all know that the Hebrew/lunar calendar and the general/solar calendar cover the same amount of time, but with a different pattern of organization. The Hebrew day and the scientifically-measured day are also slightly different. While both are 24 hours long, the "hour" in Talmudic terms is flexible – one-twelfth of daylight is an hour, and one-twelfth of darkness is an hour. Except at the equinoxes, therefore, there is always a discrepancy between the length of a day-hour and a night-hour.
I remember being very excited as a student to learn that the rabbis had been among the first to declare that the world was round, hundreds of years before Columbus. My excitement was short-lived as I discovered that "round" did not mean "spherical." Rather, they believed the world to be shaped like a plate, and that the sun and moon rotated around it on a daily basis.
All of this information seems somewhat irrelevant to the use of this word in prayer, except that it begs the question why this particular unit of time was chosen rather than the minute, hour, week, month or year. In this particular location, the "day" seems to allow for times that God's holiness is proclaimed–-and times that it is not.
Perhaps the notion is that we live in many different realms in twenty-four hours. God's presence can be felt in each one. Or perhaps the notion is that no day should pass without the praise of God. Or perhaps the reassurance is that there are times for everyone and everything in the course of each day when God is praised and, by extension, times when our attentions are drawn elsewhere.