That's the name of a well-known movie from Mexico and also happens to be one of my biggest favorites. But I have always struggled to understand how it translates to "Maria, Full of Grace" in English. What purpose is that "eres" serving there? Shouldn't it just be called "Maria, Llena de Gracia"?
Because that's how the original prayer was translated to Spanish. In English, the same prayer is translated "Hail Mary, full of grace", hence the English translation matching the common English prayer.
Longer answer (regarding the syntax)
Modern Spanish generally uses what's called a SVO structure (subject-verb-object), and more specifically what could be called SVDI (subject - verb - direct object - indirect object). This is seen in sentences like "S(Juan) V(dio) D(los libros) I(a María)". That said, Spanish does allow free ordering of those four elements. The only restriction is that if the objects come in front of the verb, they must — with a handful of exceptions — also be included as an object pronoun (hence, the IOVD option "A María los libros se los dio Juan" obligates se los in front of dio).
The other type of element that can move around freely (besides adverbs — out of the scope of this response) are predicative nominatives. They function like (in)direct objects most of the time with a few small differences. The sentence you're asking about is "llena eres de gracias". Llena represents a predicate nominative. Summed up, we have PnV with implied S (tú). We could respin that and get SVPn which is more common: "Tú eres llena de gracia". We could also do VSPn: "Eres tú llena de gracia".
Some sentence structures are quite common. OVS is of course the norm with gustar-type verbs. SVO is common for declarative. VOS is most common for interrogative. Others are heard frequently, even if not the default. Some of the rarer orders will normally be used when you want to give particular emphasis to one element or another, although it's difficult to explain the exact rules governing that and I'd recommend just going with what you see others use for contrast/emphasis.
Longer answer (regarding the use of ser)
While indeed at first glance it may seem like the verb should be estar, this is one where you can't think look at ser as permanent and estar as temporary . Also, it's important to remember that while some adjectives will almost always be used with one or the other, others can have drastic changes in meaning. When in doubt, one thing I've found is you can often sneak in the word "una persona" / "una mujer" / un hombre" before and the rationale for ser will pop out pretty clearly (and also completely contraindicate estar)
 One of the main differences is that its object pronoun is generally the neuter "lo": ¿Es María llena de gracia? Sí, lo es. (although, in reality, you'd rarely use the lo in this case). Also, a predicative nominative generally doesn't ever appear with its object pronoun simultaneously.
 That's probably one of the worst ways, actually, to describe the difference between the two because of the proliferation of contraindications. If any quick difference is to be used, I'd recommend going with the English cognates: state/estar, and essence/ser. The nature of pizza (its essence) is that it's hot, while ice cream is cold. Hence "La pizza es caliente y el helado es frío" when describing them generally. But the state of something need not line up with its nature. My slice of pizza may be hot or cold, and in describing that state, I'll use estar
Actually "Maria llena eres de gracia" it's a part of a prayer dedicated towards Mother Mary called "Ave María" or "Hail Mary".
"Dios te salve María llena eres de gracia el Señor es contigo; bendita tú eres entre todas las mujeres, y bendito es el fruto de tu vientre, Jesús. Santa María, Madre de Dios, ruega por nosotros pecadores, ahora y en la hora de nuestra muerte. Amén"
As for why the word "eres" is in that sentence, I'm inclined to say that is old Spanish, since this prayer is taken from the bible. It's a way of saying you are full of grace. If there is anyone who can confirm this that would be great. Hope this helps somehow!
It's The "Hail Mary"
María, llena eres de Gracia is not translated Mary, full of Grace.
The word eres means off course you are.
If you translate Mary, full of Grace to spanish then you'll have María, llena de Gracia.
So the real purpouse of eres is because it is a prayer, a phrase you are ACTUALLY saying to her, as you were talking to someone in front of you. The correct way that prayer would be translated to english is Mary, you are full of Grace (talking to her), because if you say Mary, full of Grace it could be understood as you are refering to a third person not a second as the real purpose of that phrase is.