Latin is the primary liturgical language of the Roman Catholic Church’s Western tradition.
The Roman Rite developed within the Latin-speaking western part of the Roman Empire. Latin gradually replaced Greek in much of the Western Church, becoming the principal language of worship, theology, canon law, and administration. The Church’s Latin is often called Ecclesiastical Latin because its pronunciation and usage developed within Christian institutions.
The Second Vatican Council’s reforms in the 1960s allowed much greater use of local languages in the liturgy. Latin, however, remains the official language of the Holy See and continues to be used in Church documents, ceremonial contexts, and some celebrations of the Roman Rite.
This answer concerns the Western Catholic tradition. Eastern Catholic churches may use Greek, Church Slavonic, Arabic, Syriac, Armenian, or other liturgical languages according to their traditions.