The First Three Days of the New Year (正月三が日)
The first three days of the New Year refer to January 1, or New Year's Day, and January 2 and 3 of every year. They are also called simply "the first three days."
"Gantan" and "Ganjitsu"
Both words refer to January 1, but they are used for different hours of the day.
This is the word for dawn and morning of January 1. In some area, "gancho" is used instead of "gantan."
This is the word for the whole January 1. It is also the name of the Japanese national holiday which falls on this day.