I've heard that many Roman Catholic churches still hold Mass services and particularly ceremonies (e.g. weddings) in Latin. Is this true, and if so why is Latin considered to be a better language than the native language of the country the church is in?
Yes, prior to the promulgation of the Novus Ordo Mass finished by 1970, Latin was the language used at Mass throughout the world. The change to the vernacular didn't change the official language of the Catholic Church which is Latin.
Many parts of the Mass are still (or can be) proclaimed in Latin. If you've got some time, watch or listen to the Mass on EWTN. I think there's a lot more Latin in that Mass than there is in the average town's parish. I think there are at least two reasons for that:
Beyond that, it was obviously the desire of Mother Angelica to have a more traditional (and therefore holy, beautiful and sacred) liturgy. But it doesn't make it more "meaningful"; Christ isn't less present at Masses proclaimed in the vernacular.
In 2007, Pope Benedict XVI issued a Motu Proprio Summorum Pontificum (only in Latin) in which he said that it was OK by him if people used the old Roman Missal (only in Latin), which incidentally is less than 10 years older than the new one, for their Mass. This lifted the responsibility from the Bishops to say yes or no and made a few Traditional Catholic groups happy.
But he made it clear that this is the "Extraordinary Form" of the Mass, not the Ordinary one. And, every time you hear the word "Extraordinary" in the Catholic Church, it indicates something that is not really necessary for salvation in general, but good for some circumstances. (Extraordinary Ministers of Communion, Extraordinary means of Baptism, etc...)
It's not more holy, in the sense that it is "special in God's eyes". But it certainly is more holy in the traditional sense of the word "set apart", more so today than in the hey day of the Holy Roman Empire.
But, it is the official language of the Church and as long as the Pope is in Rome, it always will be:
As a very preliminary point, there are several "Rites" within the Roman Catholic Church1 and some of them have never had, and never will have, Latin liturgical services. So all of the below applies specifically to the Roman Rite (which is the most widespread by far).
To lay the basic groundwork: Latin is still the official liturgical language of the Roman Rite. The Scripture readings in the liturgy are translated from various sources, but apart from those, any non-Latin text of any liturgical service has been translated from the official Latin, and the translation itself has been approved by the Vatican.
That said, the everyday liturgical use of Latin is rare and typically confined to monastic or academic settings, and only to a few such settings. In normal parish life you will generally encounter Latin in one of three ways (ordered from most common to least common):
As to why Latin is considered a "better language" there are many answers. Popes Pius XI and John XXIII both solemnly affirmed the general importance of Latin in the life of the Catholic Church, in letters published respectively in 1922 and 1962. They identified, among other things, its universality, immutability and nobility -- not to mention that knowing Latin unlocks a huge treasury of Patristic and ancient literature.
There are also many reasons why an everyday Joe who can barely manage his own native tongue might prefer to worship at a service conducted in Latin. Peter mentions beauty and that's an excellent one. Some of the Latin prayers of the mass have been with us for a thousand or more years precisely because they are exceedingly well-crafted poetic gems. Likewise many long-lived and beautiful sacred-music settings were written for, and best fit, Latin texts.
I would guess that an Orthodox Christian could speak at length on the question of liturgical beauty -- there is a strain of thinking that is muted in current Catholic discourse but I think very strong with the Orthodox, wherein one considers the beauty of a liturgical service objectively or theologically, rather than subjectively or pastorally. From this perspective, the question is less "what is accessible to the people present?" and more "what is most fitting for the Eucharistic worship of almighty God?" This gets complicated, of course, because vernacular liturgy is fairly well-established in the Orthodox Churches.
I mentioned tradition above -- the Catholic Church is big on that, and worshipping in Latin, using the same words that our fellow Catholics have used for a thousand or more years, connects us with our tradition very concretely.
And if I might speculate a bit: Another reason for some people may be that a veil between the worshiper and the act of worship (in this case an intellectual veil) may actually facilitate one's interior participation in that worship. The parish priest who wrote this little book, for example suspects that a surprisingly large number of people actually find themselves in a state of continual distraction when attempting to worship God at a liturgy that is entirely spoken aloud in their own language. Of course this gets into contentious questions about the theology of worship, what it means to "participate", etc.
1 A "Rite" is a coherent liturgical and theological tradition that is usually connected with some particular culture -- non-Latin examples include the Maronite and Byzantine Rites. There are even a few non-Roman Latin Rites