This is the 3222nd most frequent Russian word.
новогодних
"Новогодних" means "New Year's" (genitive or plural form, related to New Year).
In this sentence, 'новогодних' is a genitive plural adjective modifying 'праздников' (holidays), indicating that the holidays in question pertain to New Year's.
Представьте себе магию новогодних праздников.
Imagine the magic of New Year's holidays.
Here, 'новогодних' is a genitive plural adjective modifying 'гирляндами' (garlands) to describe garlands that are associated with New Year's decorations.
Мы украсили дом новогодних гирляндами.
We decorated the house with New Year's garlands.
In this example, 'новогодних' is a dative plural adjective modifying 'подаркам' (gifts), showing the relation of the gifts to the New Year's.