Zontar said:
It's more of a joke in reference to the fact that Japanese broadcasters use 24:00-29:59 instead of 0:00-6:00 between midnight and 6am. I don't know if anything else uses it though.
24:01 and forward is an unofficial standard (at least I think it's unofficial, I can't remember ISO 8601 mentioning it or anything else big) for times after midnight. 0:00 is midnight
start of today and time progresses until 24:00 which is
end of today or tomorrow's 0:00. These are part of ISO 8601 - 24:30 is, not often, but often enough to be semi-official notation to mean "half an hour after today". Similarly, 27:00 would be "three hours after today" or "three o'clock tomorrow". It's used to unambiguously distinguish between two times if you need to roll over a new day during the operation. So, for example, if you start a log on, say, the 10th of the month, if you were to note something happening at 27:00 it's unambiguous whether you mean 03:00 on the 10th or 03:00 on the 11th, as opposed to, you know, using 03:00.
It's just that there aren't that many situations that require the post-today notation, so it's not that widely used. It's definitely out there, though.
OT: I use 24 hour clock. More convenient. Easier to know exactly what time it is. Frankly, I'm even up to using some sort of decimal time system, as it's going to simplify things A LOT. I just can't find any nice watches that support it.