Original: A typical usage is giving opening hours ending at midnight, e.g. "00:00 â" 24:00 "," 07:00 â "24:00". Similarly, some railway timetables show 00:00 as departure time and 24:00 as arrival time.
Simplified: For example, you would say "Tuesday at 24:00" and "Wednesday at 00:00" to mean the exact same time.