RORY: You know I bet you can tell a lot about people from their garbage … It talks about their eating habits, what they read, do they go to concerts, are they responsible, do they pay bills on time?
LORELAI: Yeah, you do know honey, that garbage doesn’t actually talk at all unless it’s on Sesame Street.
Sesame Street is an educational children’s television program for preschoolers which has been broadcast since 1969, and combines sketch comedy, short films, and puppetry using Jim Henson’s Muppets; humour and pop cultural references are used to help communicate its messages. One of the most popular and widely-watched children’s shows, it has won multiple awards, including more than a hundred Emmys and several Grammys – more than any other children’s program.
Lorelai is most likely referring to Oscar the Grouch, a green Muppet who lives in a trash can and periodically pops up to complain about something, usually ending by telling everyone to leave him alone and get lost.