This system is referred to (only in the US and the English speaking parts of Canada) as military time or (only in the United Kingdom and now very rarely) as continental time. In some parts of the world, it is called railway time. Also, the international standard notation of time (ISO 8601) is based on this format.
A time in the 24-hour clock is written in the form hours:minutes (for example, 01:23), or hours:minutes😖econds (01:23:45). Numbers under 10 usually have a zero in front (called a leading zero); e.g. 09:07. Under the 24-hour clock system, the day begins at midnight, 00:00, and the last minute of the day begins at 23:59 and ends at 24:00, which is identical to 00:00 of the following day.
12:00 can only be mid-day. Midnight is called 24:00 and is used to mean the end of the day and 00:00 is used to mean the beginning of the day. For example, you would say "Tuesday at 24:00" and "Wednesday at 00:00" to mean exactly the same time. However, the US military prefers not to say 24:00 - they do not like to have two names for the same thing, so they always say "23:59", which is one minute before midnight.