I will try to explain (I am not Greek!!!)
There is two forms of possessive pronouns in Greek - weak (αδύνατος τύπος) and strong (δινατός τύπος). As a weak form are usually used words μου, σου, του, της, μας, σας, τους (my, your, his, her, our, your, their). As a strong form are used the "pronoun adjective" δικός, ή, ό with the same words, as for weak forms - δικός μου, δικός σου, etc. Both forms are used to show the fact of owning, but strong form is additionly used in next cases:
1) absence of defined word. "Τίνος είναι αυτό το βιβλίο; - Είναι δικό μου" (Whose is the book? Is mine)
2) to emphasize the fact of owning. "Η δική μας αίθουσα δεν είναι άσχημη" (Our lecture hall is not bad)
3) to show the contrast/contradistinction. "Δε θέλω το δικό σου βιβλίο, θέλω το δικό μου" (I do not want your book, I want mine)
This information was taken from Greek textbook written in my native language, so I apologise in advance for possible mistakes in my translation to English.
Also I will be gratefull to Greek native speakers for any remarks))