This is an online video version of Disney/Pixar's Little Match Girl, a short. For a better quality version, you can find the short as an extra on The Little Mermaid (Two-Disc Platinum Edition) from Disney.
The music is by Alexander Borodin (String Quartet No. 2 in D Major: Third Movement: Notturno) and a lovely choice. I'm partial to Borodin myself because he's one of my husband's favorites. He loves the Polovtsian Dances.