14 CFR 1.1 defines night as the period between the end of evening civil twilight and the start of morning civil sunrise. This definition is again referenced in 14 CFR 61.109. Therefore day is defined as the period between the start morning civil sunrise and the end of evening civil twilight.
That being said the regs also refer to night time as between sunset and sunrise and 1 hour after sunset and 1 hour before sunrise (14 CFR 61.57).
As I understand it, 14 CFR 1.1 is the official accepted demarcation between daylight and night time for the FAA; however it's not used as a standard when say defining when night currency is applicable or when to use exterior aircraft lighting, primarily because of interference from ambient lighting at dusk and daybreak affecting airman prowess during this time.