Hello,
The girl that Miley Cyrus kissed is Katy Perry.
This took place in February 2014 at Miley Cyrus' LA 'Bangerz' concert. Which included a star studded audience, with the likes of Nicole Richie, Hilary duff and Christina Aguilera watching by for the controversial moment.
It was expected that 21 year old Miley would indeed cause some type of controversy, as she has been known to be rebellious throughout her recent career. Combining this with Katy Perry who is known for singing hit song "I kissed a girl and I liked it", it seemed the perfect opportunity for Miley to take her up on the suggestion!
Following the kiss, Katy Perry is said to have tweeted a picture of herself and Miley giggling post kiss.
I hope this answers your question!