The woman in Woman on the Edge of Time refers to the main character, Connie. She's a woman (check!) on the edge of time (check, check!): she's visited by people from the future and then she goes and visits the future. So she's a special, receptive, telepathic, kind-of-sort-of superhero.
Though, now that we think about it, you could really say everyone is on the edge of time; the future keeps zipping out ahead of you, and you keep falling into it. So the title could be seen as being about Connie's special abilities. But (especially since we're never totally sure that Connie has special abilities to begin with) it could also just be a metaphor for how everyone is balancing precariously between past and present.