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.
Emily: (about Lorelai's shade of lipstick) That's a pretty color. What's it called?
Lorelai: "Vicious Trollop."
Emily: Now why do you say things like that? (Lorelai shows her the lipstick tube). Now why would you name a lipstick that?
Lorelai: Because "Dirty Whore" was taken.
Emily: (about the man that Lorelai got pregnant with at 16) Your father would have gotten him a job with his insurance business, and you two would be living a lovely life right now.
Lorelai: Christopher didn't want to be in the insurance business, and I am living a lovely life right now.
Emily: Oh yeah, far away from us.
Lorelai: Oh, here we go again.
Emily: You took that girl and completely shut us out of your life!
Lorelai: You wanted to control me.
Emily: You were still a child!
Lorelai: No, I stopped being a child the minute the strip turned pink, okay? I had to figure out a way to live. I found a good job.
Emily: As a maid! With all your brains and talent!
Lorelai: I worked my way up. I run the place now!