LORELAI: Will you help me push other people out of the way if they’re going for my size [at the shoe sale]?
RORY: I’ll even run interference for you.
To run interference is a term from American football or gridiron, meaning to legally block opponents in order to create a clear path for the ball carrier. As as idiom, it means to help someone while they perform a task without directly intervening, such as deflecting attention away from them so they can work in peace. Rory may be literally planning to block people at the shoe sale though, giving Lorelai a clear path to the sales desk.
The Annotated Gilmore Girls 