The Latin Rite is the name given to the rituals, customs and laws followed by the "western" Roman Catholic church. Unfortunately, "Roman Catholic" is an ambiguous term. Sometimes it refers to all churches that are in full communion with the Pope and who acknowledge that all Christians owe obedience to the Pope, including the Eastern-rite Catholic churches. But in the present context it means the body of Catholics in "western" countries who are subject directly to the Pope in his role as Patriarch of the West (about 98 percent of all Catholics), and not to the Eastern-Rite Catholics who are indirectly subject to the Pope by being directly subject to the Eastern-Rite Catholic Patriarchs. The differences between the Latin Rite and the Eastern Rites are not in matters considered infallible dogmas, but are in rules of discipline and custom, the Eastern Rites following usages similar to those of the Orthodox churches.
Latin-rite Catholic priests must be celibate. Eastern-rite Catholic priests, like Eastern Orthodox priests, may marry before they are ordained, but if they do so, they may not become bishops. In Latin-Rite Catholic jurisdictions, the sacrament of confirmation may, with some exceptions, be licitly performed only by a bishop, and is usually given only to persons old enough to understand the importance of the sacrament. In Eastern-rite Catholic churches, that sacrament is administered by parish priests to newly baptized infants via the rite of chrismation.
The Latin Rite is so-called because until the 1960s, Latin was used as the liturgical language in Catholic churches in "Western" countries. The Second Vatican Council decided that the vernacular would thenceforth be used instead.