This is the 55th most frequent French word.
premier
"Premier" means "first" in English.
Here, 'premier' is used as an ordinal number, indicating the first element in a sequence (in this case, the day of the year).
Le premier jour de l'année est toujours célébré.
The first day of the year is always celebrated.
In this sentence, 'première' (feminine form of 'premier') acts as a superlative indicating superiority in order (arriving first).
Elle souhaite être la première à arriver.
She wants to be the first to arrive.
'Premier' in this context is used to denote the debut or initial instance of something (his first novel).