“I have died everyday waiting for you
Darling don't be afraid I have loved you
For a thousand years
I'll love you for a thousand more”

Christina Perri – A Thousand Years Lyrics on LyricsMode
This girl have loved this guy but maybe the guy doesn't like her back or still having an relationship with some other girl. The girl that sing this song have promised that she will love the gut forever and comforting the guy that there's other girls that cared for him and loved him, so the girl who sing is saying don't be afraid when the girl who the guy is having an affair with left the guy.
She has waited for a long time for him to tell her he loves her. But she has loved him ever since they met (which felt like a thousand years). And she will love him forever.
This is like a metaphor that symbolizes the amount of years that Edward has waited for Bella.