In the novel The Bell Jar, written by Sylvia Plath, we can notice the idea of "the personal is the political." What does it mean, and how exactly can we perceive it in this novel?

The Bell Jar, first published in 1963, is a quasi-autobiographical novel that expresses many of the themes that are typical of the feminist movement of the 1960s. The protagonist, Esther, who represents the author herself, is a young woman who is struggling to become a writer and also struggling with mental illness. While these might seem like personal matters, what the phrase "the personal is the political" suggests is that Esther's struggles are as much against the patriarchy as purely personal ones.
As a talented young writer, one of Esther's major opportunities is an internship with a women's magazine. She does not have the wide range of choices open to a male writer—her most prestigious opportunity as a leading student of an elite college is writing about makeup and fashion and similarly "feminine" topics, rather than things that make more use of her skills and talents. She is appalled by the typically female roles offered for a young, educated woman, such as stenography, teaching children, or becoming a traditional wife and mother.
Esther's mental health issues are not described as purely personal. Rather, their origins are grounded in the political—namely, the lack of equal opportunities for intelligent, creative women and the culture of discrimination, rape, and sexual exploitation.