True story:
In the game, the song is supposedly written by Julia Heartilly, a pianist who is the love interest of Laguna Loire. She has a conversation with Laguna which assumedly inspires her to write and perform this song.
Accompanied by his close friends Kiros Seagill and Ward Zabac, Laguna often visits a hotel lounge in Deling City in Galbadia where Julia performs piano and sings. Laguna always sits at a table around the corner facing Julia, shyly gazing her with much admiration, thus the lyrics:
"I saw you smiling at me
Was it real or just my fantasy?
You'd always be there in the corner
Of this tiny little bar"
One night after Laguna's usual visit and his failed attempts to initiate talks with Julia due to his intense shyness and nervousness, much to his surprise, Julia invited him to her hotel room where they had a pleasant conversation. Not until much later did they know that this was their last meet, as Laguna soon went on a mission to Esthar but probably got lost in Lunatic Pandora facility thanks to his usual clumsiness. This led to serious injury of his body that took half a year to recover, nursed by Raine and Ellone in a peaceful small village. Not knowing this, Julia broke her heart mistaking him for being killed in the mission. She eventually married General Caraway and gave birth to Rinoa Heartilly. Unwilling to disturb Julia's then assumed happy family, Laguna decided not to reappear in front of her. Julia later died in an automobile accident when Rinoa was 5 years old. Julia and Laguna's last encounter at the hotel probably inspired her the lyrics:
"My last night here for you
Same old songs, just once more
My last night here with you?
Maybe yes, maybe no
I kind of liked it your way
How you shyly placed your eyes on me
Oh, did you ever know
That I had mine on you?"
Chronologically later in the game, the song becomes the reflection of the unfolding love story between the two protagonists, Squall Leonhart (heavily hinted but not stated outright as Laguna's son), and Rinoa Heartilly (Julia's daughter). The song is heard repeatedly throughout the game as various remixes though no lyrics are heard. Its full version can be heard during Squall's and Rinoa's lonely moment at the Ragnarok Airships.
Julias song:
http://www.youtube.com/watch?v=LocdLRZqICE