Emily Gilmore is Lorelai's mother and therefore Rory's grandmother. Emily had a limited relationship with her daughter as an adult, until they began to bond again with Rory needing money to get into Chilton Prep.
Emily was raises with a strict social code, attended Smith College, and is extremely wealthy. As a result she is constantly disapproving of her daughter's choices.
Although she's happily married to Richard for most of the series, they have a separation during season five and end up back together.