This quote is taken from Act III, Scene V, and is spoken by Juliet's mother, Lady Capulet. To put this into context, Juliet has refused to marry Paris, and her parents are both annoyed and exasperated by her feelings on this subject.
In terms of its literal meaning, Lady Capulet is saying here that her daughter is a "fool" for not wanting to marry Paris. Moreover, Lady Capulet wishes that Juliet were dead and, therefore, married to her grave. Looking deeper, Lady Capulet's fury is apparent: she cannot understand why Juliet would refuse such a handsome and successful suitor. She is so angry that she would rather see Juliet dead than have her daughter continue on this path of complete defiance. After all, in this setting it is a woman's duty to get married and to have a family. By marrying well (with Paris), Juliet ensures the prosperity and respectability of the Capulet name and the Capulet family.
Of course, Lord and Lady Capulet have no idea that Juliet is refusing Paris because she has already married Romeo and, earlier in this scene, has consummated that marriage.
This line is spoken by Lady Capulet (Juliet's mother) in Act III, Scene 5. She says it about her daughter. What she is saying (and this is really a terrible thing to say) is that she wishes her daughter were dead.
She says this because she is mad at Juliet. She is mad because of the fact that Juliet does not want to marry Paris when that seems like such a wonderful match to her parents.
By saying this, Lady Capulet is sort of foreshadowing what will actually happen to her daughter -- she will soon be dead, just as her mother is wishing for in this passage.
Additonally, this statement is both ironic and foreshadowing because the next time Lady Capulet sees Juliet she will place her in her grave on the day of her planned marriage to Paris. Juliet is most likely burried in her wedding clothes that she had put on before drinking the potion. Therefore she was "married" to her grave.
"Married to her grave" also links back to the theme of fate and "star-crossed" lovers, because it is kind of saying that Juliet cannot escape her fate of dying and becoming "married to her grave."