EMILY: Look at these flowers. Baby’s breath. What is this, County General?
Baby’s breath (Gypsophila paniculata) is a popular ornamental flower native to Central and Eastern Europe with clouds of tiny white blooms in the summer. It’s often used in floristry to provide a backdrop for larger flowers.
“County General” is a common name for hospitals in the US eg Roebuck County General Hospital. In real life, there isn’t a hospital with this name in Connecticut.
Emily seems to think baby’s breath is only suitable as part of a flower arrangement you’d give to someone in hospital, lacking the elegance required in a formal setting. You can see how standards have dropped in Hartford society without Emily’s capable hand on the tiller.
The Annotated Gilmore Girls 