Amanda is Phoebe and Monica's old roommate, she appeared in The One With Ross' Tan, when she comes to visit the two from England. The New Yorker (from Yonkers), has attempted to pick up an English accent (but quite often fails, sounding awful in the process - for example saying "I feel like a perfect arse") and is pretty much of an ego-centric, but in spite of her annoying nature, when she calls Monica's apartment and, after Chandler takes the call and bemuses Amanda by revealing to her that he takes pedicures before handing the phone to Monica, she and Phoebe agree to meet up with her in the coffee shop so as not to hurt her feelings. There, Amanda inadvertently lets out that Phoebe wanted to cut Monica out of her life in 1992 (before the series started) as Monica was at the time driving Phoebe mad by being, as Phoebe later puts it "controlling and compulsive and shrill". Monica is upset about this, but Phoebe explains to her how she's glad now that she changed her mind after realizing what a nice person Monica really was despite all of this. The two make up.
It is never revealed exactly why Amanda moved away from Monica and Phoebe, but given her inflated ego and self-absorbed attitude, it is likely that she, like Phoebe at first, couldn't stand Monica's controlling, compulsive and shrill nature. She seems to really like both Monica and Phoebe however, probably because she knows they're nice people really, seeming genuinely pleased to see them both again and looking genuinely upset when she realized she'd upset Monica, when it became clear that Monica was hearing that Phoebe had wanted to cut her out of her life in 1992 for the first time.