Well, you got me interested, so I did some research.

Until the 15th and 16th century and the advancements in mechanical clocks that happened in that era, personal timekeeping devices were not that common. If you could actually pinpoint when exactly in the day is 2pm in that time, you probably had some kind of a sundial available. Hourglasses existed, but there are no records of them existing in Europe at the time, and they aren't exactly useful for tracking time over the length of a day. Candle clocks and incense clocks existed in China, but it does not seem they were too widespread or advanced. Water clocks were also a thing, but I can't seem to find any good sources concering how accurate or widespread they were. At any rate, if you had a clock at the time, you were probably a priest of some kind (temples need timekeeping for prayers), or had a sundial at the city square.

As for tracking days? Well, there were actually a bunch of regional calendar systems at the time. They were needed in some way or shape; after all, tracking things such as the harvest season is necessary for proper farming. If you were in formerly Roman Europe, you probably used the Julian calendar. If you tracked years, you probably had a system based on the reign of your land's ruler; the Anno Domini system only came to existence in 525 and took a lot of time to spread. Can't tell you much else, because finding any sort of a source regarding 6th century calendar usage is proving to be a problem. Reading material would be appreciated.

So, in conclusion? Meeting in 2pm in a week's time would most likely go along the lines of "meet me some time after noon in seven days, and don't bloody forget."

Sources:

History of Time by Keith Flamer

Keeping Time: The Origin of B.C. and A.D.

Probably something not from those sources, too. This took a surprisingly long time to compile. Sorry if this breaks any rules, mods.

Not only would you have no reference for 2pm, you wouldn't have a conception for that kind of time.

This disparity still exists today, often in the form of "Island Time" versus, let's call it "western time". The more technical terms would be "polychronic time" and "monochronic time". Most pre-industrial cultures would have had a polychronic view of time. It would be very difficult to get someone to recognize the importance of a time that was precise down to the minute or the second, because such a thing, such a monochronic view of time and such an importance on temporal precision, doesn't really exist in their world, nor is it a priority. For people with that view of the world, the idea of being "early" or "late" to a meeting during the day is not something they have the cognitive framework to care about.

Let's say that there was a large tree near the center of your village, and at some time after noon the shadow of the tip of the tree just touched a fence, giving you the ability to reference a specific time of day (since you have no clock, nor do you really have a concept of hours in 600 CE). Even if you told your friend "in one week's time, meet me back here when the shadow of the top of that tree touches that fence over there" the chance of your friend showing up exactly then is virtually nil, unless for some reason they had become fascinated by the tree's shadow and sat there for a long period of time waiting for it. They simply would lack the primacy of importance placed on precisely timed meetings.

I don't think you'd have that strong an idea of a 24 hour day, although 24-hour clocks date back to at least 1410, and is based on the Egyptian decan astrological system.

But I can't really answer your question. Actually, I'm here for follow up questions: would the uneducated masses have a day partitioned into 24 equal parts?

From Wikipedia:

The earliest country to introduce the 24-hour system nationally was Italy,^[citation ^needed] in 1893.

Does this mean that before 1983 it was used by certain social strata, or say the military, exclusively?