Technically, the sun doesn't shine at *clock* midnight everywhere in Alaska. But in summer, north of the Arctic Circle (e.g., Utqiaġvik/Barrow, Fairbanks vicinity), the Midnight Sun phenomenon occurs.
Due to Earth's axial tilt, the sun remains above the horizon for 24+ hours a day during summer weeks. At solar midnight, the sun dips to its lowest point but stays visible—creating endless "daylight."
South of the Arctic Circle (Anchorage, Juneau), summer nights are very bright (civil twilight), but the sun does set briefly.