Archetypes are very exciting, because, theoretically speaking, they're supposed to be symbols that are universally recognizable. Archetypes are prototypes – stock roles or character types that carry a lot of associations. In literature, a lot of these archetypes come from mythology or folklore, but really they're being created all the time. So take "the hero," "the princess in need of rescuing," and "the John Cusack (romantic love interest) type" for example. All archetypes.
Anyway, back to Mango Street. The three sisters who examine Esperanza's hand and foretell her future call to mind the Fates – the three ancient sisters in Greek mythology who spin, measure, and cut short the thread of every human life. In some traditions, they show up three days after a child is born in order to foretell the infant's future. They know everything that will happen to an individual during his lifetime, including the moment he will die, so they're often associated with destiny and mortality.
So, it's no coincidence that Esperanza meets the three sisters at a wake for a baby – after all, it's sort of the job of the Fates to show up at births and deaths. So here they are, doing the whole birth and death thing, and they encounter an ambitious little girl, our heroine, Esperanza. They can sense how weirded out she feels about being at a wake, because "they [have] the power" (41.5). So they offer her a stick of gum, examine her palm, and manage to guess her secret desires. Because of their mythological power, the sisters' confirmation of Esperanza's plans to escape Mango Street give us confidence that she'll actually make it. And after the previous two chapters, in which Esperanza is raped and Sally gets married to a macho loser, we could use some cheering up.