The Latin translations of the Lords Prayer are well known, especially in the Roman Catholic church where masses were historicaly done completely in Latin, a few churches continue to do so. There are several translations which vary in wording. Realize that from the original Aramaic (which isn't recorded) to the Greek found in the New Testament, there are two versions - one in Luke the other in Matthew. The various Latin translations differ primarily in the wording of daily bread and the line regarding temptation.

The following Latin is from The translation into English is my own.

Pater noster qui es in coelis,
Father our who is in heavens

Pater literally means 'Father', and is the object of 'Our' as a possessive. qui is the masculine nominative form which is translated to "who". In almost every language, 'to be' is an irregular verb, this is true of Latin too: "sum, es, est, sumus, estis, sunt". Coelis is heaven, or more aptly, everything above the earth. This word applies to the sky, space, weather, universe though is most often used in conjuction with deities.

sanctificetur nomen tuum,
be-hallowed name your

sanctificetur is the present, passive, subjunctive but thats a bit much to keep track of - Latin is like that. sanctificetur means to sanctify and treat as holy and is the original root of the word 'sanctify'. nomen covers more than just the idea of "name" and includes the ideas of family name and title. With individuals it also refers to what you write in a debt ledger (as opposed to what people call you). Tuum is simply the singular neuter possessive adjective "your" applied to name (which has no gender).

ad veniat regnum,
Come kingdom

ad veniat means "to come", "arrive at", "reach", "be brought". This word should be familiar to many in the word "Advent" which is the time of preparation for Christmas. Regnum means kingdom, but it also extends to the area of regal power (once again, the Latin roots showing)

fiat voluntas tua in terris sicut in coelis,
be-done will your in Earth as in heaven

Fiat means to make happen and can be seen in many other romance languages - font in French, fanno in Italian. voluntas deals with the will and is seen in English with "voluntary". Tua is similar to tuum (above) except this time is feminine form. Just as coelis refers to everything above the ground, terris refers to the ground itself but not "Earth" as the planet. Sicut is simply a conjunction meaning like or as though extends to a few other 'ideas' such as 'as it certainly is'

panem nostrum quotidianum da nobis hodie,
bread our daily give us today

The word for 'bread' has changed very little from Latin to Italian, from panem to pane meaning bread or loaf. Quotidianum means daily, regular, and habitual - though it also extends to the idea of 'ordinary', 'common' and 'unremarkable'. nobis is the pronoun meaning 'we' or 'ourselves' and is otherwise unremarkable. hodie is an adverb meaning 'today' or 'at the present time' which is applied to the verb da which means in this context "grant" or "bestow" along with "give".

Et dimitte nobis debita nostra,
And forgive us debts our,

Et still means 'and' in most romance languages. Dimitte does not exactly mean "forgive" in the context that we consider it today, but more oft he idea of sending away, scattering or dismissing. Debita is the root of the modern day word "debt" and is partially responsible for the older English translation that reads "and forgive us our debts".

sicut et nos dimittimus debitoribus nostris
as and we forgive debtors our

In the line before, dimette was used - the present, active, imperative, second person singular; in essence "(you singular) dismiss". Here, it is the present, active, indicative, first person, plural meaning "(we plural) dismiss". In this second form it is not a command. Akin to debita above, debitoribus is the plural form of 'debtor'.

et ne nos inducas in tentationem,
And not us lead into temptation,

The first interesting word here is that of inducas. This word means lead, but not as a guide but more of a 'induce' and 'influence' - inducting. tentationem is literally that of temptation, the word is a near perfect translation.

sed libera nos a malo,
but free us from evil,

sed is a conjunction that encompasses the idea of "but" though extends to "however" and "but in fact" or other similar permutations. The implication with sed is that the part following it is the truth. libera is the basis for the modern English word "liberty". It means to free or release as a verb. In this translation, malo is used. While this does mean 'evil' it does not refer to "the evil one" as such but rather extends to disaster, misfortune, calamity, plague, punishment, and harm.

Quoniam tibi est regnum et potestas et gloria in saecula
for yours is kingdom and power and glory into ages

The doxology is not always part of the Lords Prayer, and is one of the most varied lines. It begins with the conjunction quoniam meaning "because" or more along the lines of "the previous follows from this". tibi is the pronoun 'yourself' in the singular (the "thy" form is applicable here rather than "thou"). As discussed above, regnum is the kingdom, potestas is the root of the word "potent" meaning power, force and strength, and gloria is still used today in most Christian religious ceremonies and means glory, fame, and renown. saecula has several sets of meanings that range from age as in "generation" (it would be appropriate to say that "Generation X" is a secula), but also means the past, present and future and can be translated as "forever". See saeculum for much more information on this concept and word.
Several corrections by Mortice