'New Year's Day' definitions:

Definition of 'New Year's Day'

(from WordNet)
noun
The first day of the year [syn: New Year's Day, New Year's, January 1]

Definition of 'New Year's Day'

From: GCIDE
  • New Year's Day \New" Year's` Day"\ the first day of a calendar year; the first day of January. Often colloquially abbreviated to New year's or new year. [1913 Webster]