Um, well, that "gurl" is obviously the daughter of the black-haired sensei who appeared before. That sensei seems to be an old pal of Asuka's mom, and thus it's only normal that Asuka and the "gurl" -- her name's Miyuki btw -- are childhood friends.
We have seen before, in a flashback, that Miyuki seduced Asuka some time ago. Miyuki, who is a couple of years older, introduced young Asuka to the pleasures of lesbian sex, teaching her how to kiss and lotsa other stuff. In the present, when Asuka kissed her mom, she was very surprised at Asuka's kissing skill, and wondered if Asuka had learned to do it watching porn in the Internet... to which Asuka replied that it got nothing to do with porn, that she had some real life practice (this answer made her mom terribly worried, haha). Of course, she was talking about her "practice" with Miyuki.
Miyuki's reappearance in Asuka's life may be the prelude of an attempt to rekindle that sexy relationship they used to have. Then again, maybe not. Too early to tell. We shall see.