This is the 17299th most frequent Russian word.
счастливого
"Счастливого" means "happy" or "joyful" in the context of wishing happiness.
In this sentence, 'счастливого' is used as an adjective and agrees in gender, number, and case with 'Рождества' and 'года', which are neutral singular nouns in the genitive case.
Счастливого Рождества и Нового года!
Merry Christmas and Happy New Year!
Here, 'счастливого' modifies 'пути', which is a masculine singular noun in the genitive case, following the verb 'пожелали' that governs words in the genitive case to indicate the wish.
Мы пожелали им счастливого пути.
We wished them a happy journey.
In this sentence, 'счастливого' agrees with 'дня,' a masculine singular noun in the genitive case, aligning with the structure of Russian sentences expressing wishes.