In occult terminology, a lunar day begins at moonrise and ends when the moon sets. The first lunar day always occurs at the moment of the New Moon. The second lunar day begins the next moonrise after the New Moon. It is important to note that these times are location-specific. The first lunar day for you begins at the moment of the New Moon where you are. For me, it may begin a few hours before or after depending on my location in relation to yours.
Each lunar day is lucky or unlucky for certain activities according to various lore. Which these are can vary greatly by culture.
Scientifically speaking, a lunar day is the amount of time it takes the moon to complete a full rotation on its axis in relation to the sun or to complete a full rotation around the Earth. In other words, in astronomical terms, a lunar day is the time it takes the moon to return to the same lunar phase it began in, or a full lunation, about 29 1/2 Earth days.