Rory warns Lorelai she isn’t allowed to do any Nancy Walker impressions when she meets Rory’s new boyfriend.
Nancy Walker (1922-1992) was an American actress and comedian. Rory is most likely thinking of Walker’s role in the award-winning 1970s sitcom, The Mary Tyler Moore Show. In the show, Walker played Ida Morgenstern, the overbearing mother of Mary’s best friend Rhoda Morgenstern; she reprised the role in the spin-off show Rhoda.
Rory’s comment suggests that Lorelai had previously done impressions of Nancy Walker as a joke, pretending to be the sort of interfering mother that she tried so hard not to be.