"I give my girlfriend a ring."

Translation: Eu îi dau iubitei mele un inel.

[Lacusta]

Why is the plural form used?

[cheerfulcharlie]

It's not plural. It's the noun in the dative case (and the possessive pronoun is correspondingly in the dative case as well).

[Mamemimomu73]

It is not plural form. It is dative: to my girlfriend=iubitei mele. The plural: iubite=girlfriends.

[Lajos905235]

"mele" is the female singular form in the genitive/dative -- and it lools exactly like the female plural in the nominative/accusative case

[razvan.marin]

What are you referring to exactly?