In "A Jury of Her Peers," what is symbolic about no communication with the outside world and the impact this has on a marriage?

I am not too sure I entirely know what you are asking.
Your question obviously refers to the way in which Minnie Wright was left largely by
herself in her rather bleak marriage to John Wright for so many years. This terrible
sense of isolation is something that both Mrs. Peters and Mrs. Hale mention, in
particular given the way that Minnie and John Wright had no children. Note what Mrs.
Hale says about it:

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I might 'a' known she
needed help! I tell you, it's queer, Mrs. Peters. We live close
together, and we live far apart. We all go through the same things--it's all just a
different kind of the same thing! If it weren't--why do you and
I understand? Why do we know--what we know
this minute?

Clearly Minnie
Wright's lack of contact with the outside world helped drive her to the point of
desperation. John Wright's killing of her canary and the only sound and symbol of
brightness that there would have been in their household would have been enough to push
her over the edge and to make her kill him. Clearly, it is not healthy for a marriage to
exist without much contact with other people, for both the man and the
woman.