Luke 1:28 describes the Angel Gabriel's salutation to Mary as "Rejoice so highly favored!" As Catholics, we are told this is the source of "Hail Mary, full of grace." How do we get "full of grace" from "highly favored"?
The answer is because, as they say, translation is more art than science. In modern languages certain words and phrases often do not easily translate from one language and culture to another, so you can imagine the problems that are sometimes present trying to translate a 2,000-year-old language into modern languages.
"Full of grace" is literally "pleres charitos," and that wording is used in reference to Jesus (John 1:14) and to St. Stephen (Acts 6:8). Obviously, its used with two different meanings in those two passages, but its meaning is clearly gleamed by its context. Technically, anyone who was recently baptized or received the sacrament of confession is pleres charitos.
In Luke 1:28, the word that the angel uses is kecharitomene. So its not literally "full of grace," but its root word is the Greek verb "to give grace" (charitoo). The word is the past perfect tense, meaning that the action of giving grace has already occurred. It was not something that was about to happen to her but something that has already been accomplished. The word was also used as a title. The angel did not say, "Hail Mary, you are kecharitomene" but rather, "Hail kecharitomene." Therefore the word is not simply an action but an identity.
It is thus difficult to translate because it is a unique use of the word. It has been translated by various scholars as "full of grace", "graced one," "one who has been made graced," "highly graced," and "highly favored." In the last instance the translator is using the concept that to be graced by God is to find favor with God. It would appear that any translation should use the word "grace," because that is the root word.
However, it might sound "clunky" to some—they might think "highly favored" is more title-sounding than "full of grace," and there is nothing inherently incorrect theologically about asserting that Mary was favored by God. I would consider the Immaculate Conception to be proof that Mary was favored by God.
Because of the familiarity people have with the Hail Mary prayer and the connotation that Protestant translators use "highly favored" to deny Catholic dogmas, the Lectionary for use at Mass still uses the phrase "Hail, full of grace!" But neither is technically an incorrect translation.