RORY: Why don’t you go to a wedding dress place and try a real veil on?
LORELAI: No way.
LORELAI: Too much taffeta, it gives me cotillion flashbacks.
Taffeta is a smooth plain-woven fabric made from silk. It is considered a luxurious fabric suitable for ball gowns and wedding dresses.
In American usage, a cotillion is a formal ball, often for presenting debutantes to society. However, Lorelai is most likely talking about cotillions as a class for younger girls, perhaps aged 10 to 13, to prepare them for their future debut in society. Such classes teach social etiquette, followed by a formal party where they put what they’ve learned into practice. We later learn that Emily teaches these classes, and probably taught Lorelai when she was younger.