Could anyone explain what the grammatical meaning of jí here is? I could understand the sentence Vzal sklenici z její ruky but I don't get this one.
In this sentence, "jí" would be indirect object. If you use "její", that is a possessive pronoun.
This is the difference between "He took the glass from her (she had the glass in hand)" and "He took the glass form her hand (as in: the hand belongs to her)". First one is "jí", because she's the indirect object, and second one is "její", because the hand is possessed by her.
This sentence would be more commonly used with "jí", but if you want to emphasise the hand, use "její". Though I wouldn't trouble myself with this, both forms are perfectly understandable.