MRS. KIM: This is Ho Kyung, she’ll sing with you … Watch the high notes, she’s a runner.
In singing, a run is when a singer starts off at a very high note and drops quickly down the scale on a single syllable. It’s quite a showy move, designed to feature the vocalist’s performance over the music.
You might remember Ho Kyung from the episode, “A Deep-fried Korean Thanksgiving”.
The Annotated Gilmore Girls 