Refers specifically to the morning of New Year's Day (January 1st). Often used in formal or literary contexts, such as New Year's greetings or poetry.
The clear air of New Year's morning feels refreshing.
It's a tradition to go for the first shrine visit on New Year's morning.
Compound of 元 (first, beginning) and 朝 (morning). The reading がんちょう is the on'yomi for both characters.