If you're wondering about this, you don't have to wonder for long. In the very first sentence of the book, Tomie dePaola lays it out for us. "Strega" is Italian for "witch," and "nonna" is Italian for "grandmother." So Strega Nona? She's Grandmother Witch.
It's a name that fits the main character perfectly considering the fact that the villagers whisper about her (as one would about a witch), and yet they all go to her when they need help (which makes her an awful lot like the town grandmother). She's one part mystical and one part maternal. We kind of wish she lived in our village.