Caroline was a lovely young girl, and her father was best friends with Victor's father. They were subjected to financial difficulties and moved away. During that time, Beaufort became very ill. Caroline nursed her father tirelessly, and worried about their dwindling funds. Victor's father found them and discovered Caroline and her ailing father. In the tenth month of his illness, Caroline's father died in her arms. Victor's father became Caroline's "protective spirit", and within two years the two were married despite the considerable difference in their ages.
This is probably why Caroline is so sensitive to those who are impoverished and in need of help. Caroline's sensitive nature is the whole reason why Elizabeth comes to live with the Frankenstein family.
Victor tells all of this to Robert Walton in the first few chapters of the novel.
In addition to this background information on Caroline, as a mother, she is quite "tender," and Victor describes her in the most affectionate terms possible. She is not a disciplinarian, but rather she encourages her children to pursue what interests them. When the Frankensteins take Elizabeth Lavenza in, Victor says that his mother agrees to it out of "a desire to bind as closely as possible the ties of domestic love"; she "consider[s] Elizabeth as [his] future wife" because, even as a child, Elizabeth was so gentle and loving. Clearly, his mother tried to arrange for his future happiness and seemed to always consider her children first.
Caroline is so caring and compassionate that, when Elizabeth is recovering from scarlet fever, she cannot wait to see her and she rushes in before the danger of infection is past. As a result, Caroline grows ill, and she dies soon after. However, "She died calmly; and her countenance expressed affection even in death." It is her death that prompts Victor to struggle with the notion of mortality that eventually compels him to attempt to rid humankind of death by disease.