When you hear "Magic Words", the first thing that usually comes to mind is "Abracadabra". Readers of the more recent Harry Potter novels will know "Wingardium Leviosa", "Expecto Patronum", or "Avada Kedavra" (which I believe is a variation of Abracadabra).
What then is the logic behind Magic Words?
Verbalizing an idea means putting form into something formless. It is the word that becomes the idea's body. Thus, when you have a concept, and there is no existing word to describe it, you coin a new word.
When sorcerers create spells, they create Magic Words to embody the spell. For purposes of discussion, let us use the Harry Potter example.
Now for example, centuries ago, a sorcerer discovered that he could conjure a Patronus, or a sort of spiritual familiar, which takes the form of animals. And to embody the entire spell that conjures it, he comes up with the words "Expecto Patronum".
Now to the modern sorcerer, "Expecto Patronum" may just be meaningless magical jargon, with a little bit of Latin-sounding flair. But "Expecto Patronum" actually means something, and whatever that meaning is may have been lost in the annals of history. It definitely meant something during its creation.
That's why Magic Words are never translated. They are the original vessels of ideas that came into fruition. To translate a Magic Word is to lose the essence of the idea. A translation has its own character, distinct from the original. The essence of the original becomes lost in the translation.
This is also the same reason why the Roman Catholic Church seems to have an obsession with dead languages. Some people ask, "Why is the Catholic Church obsessed with Latin? Nobody speaks it nowadays."
The reason for this what I have already stated above. Let's take the Holy Mass as an example. It is a ritual that is not biblical in nature, but one that was created entirely by the Catholic Church. The Holy Mass was created by the early Christians, and used the Latin language to embody their thoughts and ideas. Thus, in holding the Mass in Latin, the original essence of the ritual is preserved. Although translating the Mass in the vernacular will help reach more people, the Mass in Latin is the most powerful, and although I have never heard the Holy Mass in Latin, I am sure that my hair would probably stand on end, from the sheer energy of the entire ritual.