The Time Cycle in PTD2 is about the Day and Night. It shows the time along of what the atmosphere setting is. The game goes up to 24 hours. 24 hours takes 24 minutes. There are 3 time settings.
Morning - lasts 6 minutes
Day - lasts 10 minutes.
Night - lasts 8 minutes.
The time in PTD2 runs much faster than in real-life time like in the Gameboy Games.
Time stands still when you are in Towns or Indoors (Being in the PokeMart...). Time will ONLY move in areas where wild Pokemon roam (the Routes...). When you save, the game saves the exact time that you are in, when you log back in you will be right back at that time. Time does not change when you are in a battle.
You can change the time by going to Nurse Joy at the Pokemon Center in any town.
Pokemon Appearing at Different Times
Pokemon can appear at certain times and then disappear from the place at another time. Here is a full list of where they spawn.