Caroline is Victor’s mother. She adopts Elizabeth in much the same way her husband took her in – to care for her after her father passed away. She cares for Elizabeth when she has scarlet fever and catches it herself, dying when Victor is only seventeen.
Caroline may seem to be a minor character, but she’s actually hugely important in explaining Victor’s motivations and psyche. Did you notice that Victor gets really into bringing dead things to life after his mother dies? That his obsession with mortality begins with her? Victor is understandably distraught at losing his mother at such a young age; he just chooses to deal with it in a destructive and horrifying manner.
Said destructive and horrifying manner really comes back to bite him on the behind. If Victor brought the monster to life to somehow make up for his mother’s death, it is tragically ironic that this act causes the death of the rest of his family.