Why the Church still uses it, and what you are expected to know.
The Church asks that the faithful be able to sing or say the ordinary parts of the Mass in Latin: Kyrie (which is Greek), Gloria, Credo, Sanctus, Agnus Dei.
Start with the Sanctus and the Agnus Dei. They are short and you will hear them everywhere.
Knowing them means you can worship in any country on earth without a translation.
A common language across centuries and borders is a visible sign of a Church that is not merely local. It also keeps the texts stable, since a language no longer spoken cannot drift.
The Roman liturgy was Greek before it was Latin. Latin was adopted because it was the language of the people of Rome, and then kept as the language changed around it.
The Second Vatican Council permitted the wide use of the vernacular and in the same document asked that the use of Latin be preserved in the Latin rites. Both instructions are in the same text.
No one is required to pray in Latin. The Council's request that the faithful be able to say the ordinary parts in Latin is directed at parishes as much as at individuals.