I don't know about you, but when I'm dating someone, and we're in an established relationship, I like to be introduced as what I am — their girlfriend. Often times, though, men don't feel comfortable putting labels on their mate, and Emily Post agrees with this practice:
The English language may contain more words than any other, but it has yet to supply satisfactory designations for people in intimate relationships other than "husband" and "wife" and the French "fiance" and "fiancee." So begin with the introduction basics: a gracious exchange of names. Spelling out relationships in an introduction can be a distraction and may make people uneasy.
I happen to think not explaining the relationship makes things more awkward, especially for the person being introduced, but what do you think? Do you prefer to be introduced with a title that explains your relationship, or are you completely indifferent?