Hope Howell Lupin was the mother of Remus Lupin. She was a ‘beautiful Muggle girl’ who met her husband Lyall Lupin when he protected her from a Boggart in a forest (Pm).
Hope lived in Cardiff. She was very imaginative and sensitive, which was what allowed her to see the Boggart despite being a Muggle. It appeared in the form of a 'large, evil-looking man'.
She married Lyall and later gave birth to their only son Remus; after Remus was bitten by Greyback, the family's predominant worry was concealing his condition, due to the widespread prejudice against werewolves. Dumbledore allowing Remus to attend Hogwarts was something Hope and Lyall had never expected or hoped for.
Hope died at some point before the first downfall of Voldemort. (Pm)
She married Lyall Lupin c.1959. Remus was born after a year of marriage on March 10, 1960.
'Howell' is a Welsh surname meaning 'high', 'exalted' or 'the sun'. Also, it sounds like "howl", which is something wolves do. Coupled with 'Hope' this results in a very positive meaning name, possibly reflecting both her personality and appearance.
We don't know exactly when or why Hope died, but one of the pretences Remus used for his full-moon absences was that she was ill, and he had to go and visit her (PA18). Hypothetically if there was a grain of truth in this lie and Hope was in fact ill, this could have been the cause of her death, but there is no other evidence in canon to support this.