Learn Romanian: Am petrecut cea mai mare parte a vacanței la mare. - I spent most of the vacation at the seaside.

This is the possessive (or genitive) article. Normally, if the first noun has a definite article, it attaches directly to the genitive noun (like partea vacanței). But here, the phrase is cea mai mare parte. Because parte itself doesn't have a definite article at the end, we must use a (matching the feminine singular parte) to bridge the gap and mean "of the vacation".

How exactly does cea mai mare translate to "most of"?

Literally, cea mai mare parte translates to "the biggest part". The word cea forms the superlative ("the biggest"), while mai mare alone is just the comparative ("bigger"). Saying "the biggest part of" is the standard Romanian idiom for expressing the English concept of "most of" when talking about amounts or time periods.

Why is it la mare without a definite article, when the English translation says "at the seaside"?

In Romanian, nouns that follow simple prepositions of location or direction (like la, în, din) generally drop the definite article. You only add the article back if you add a descriptive modifier (e.g., la Marea Neagră - at the Black Sea). For general locations, the noun stays bare, just like la munte (in the mountains) or la școală (at school).

Doesn't the verb a petrece mean "to party"?