The bell jar is an inverted glass jar, generally used to display an object of scientific curiosity, contain a certain kind of gas, or maintain a vacuum. For Esther, the bell jar symbolizes madness. When gripped by insanity, she feels as if she is inside an airless jar that distorts her perspective on the world and prevents her from connecting with the people around her. At the end of the novel, the bell jar has lifted, but she can sense that it still hovers over her, waiting to drop at any moment.
Source: http://en.wikipedia.org/wiki/Bell_jar
I believe, Esther uses the bell jar as a symbol to convey her feeling of being cut off from the normal world because she is imprisoned within her own mind. It symbolizes the way that Esther views her world, through a distorted point of view, like looking outside from inside of a bell jar.