Ruby, Sapphire, and Emerald keep track of day and night primarily to allow Eevee to evolve into Espeon and Umbreon respectively. Unlike in other games, there are no aesthetic differences between the two.
- Day: 12:00 PM - 11:59 PM
- Night: 12:00 AM - 11:59 PM
Most other time-based events in RSE are not reliant on the time of day, but rather how much time has passed. The exceptions are thus:
- NPCs that give Berries once per day
- The Pokemon Lottery Corner's winning number changes daily
- The check for Mirage Island is performed once daily
Note that time will not pass if your cartridge's internal battery has run dry.
Time (Bulbapedia)