An 86-year-old chubby Norwegian lady with a walking stick who smokes cigars and tells witch stories – let's face it, that's just about the coolest grandma on the planet.
In some ways, Grandmamma is just like Roald Dahl. She's an adult who likes to tell stories to children. More particularly, she likes to tell stories about witches – and children. Roald Dahl might argue that she's more like his mom, though. In fact, he based the character of Grandmamma on his own mother. In any case, Grandmamma's ability to tell stories is what initially draws us in as readers, but it's also what draws her grandson in to the world of witches, setting our story on its track.
Grandmamma is a very private lady. She has clearly had some not-so-awesome things happen to her. For example, she alludes to her brother, who's not around anymore, and we know that her daughter and son-in-law both died in a tragic accident. Also, it seems as though she had a pretty traumatizing encounter with a witch when she was younger. She freezes up whenever she's asked about it. Grandmamma holds these stories very close to her, not even sharing them with her beloved grandson (and so we don't get to hear them either).
Still, despite this tough past, or maybe because of it, she's a lady open to taking risks. She lets her grandson do some crazy, dangerous things (not without a few warnings, of course) and puts herself at risk, too, by helping him along. Oh, and she takes a risk by smoking cigars against her doctor's orders. This brings us to our next point...
Boy, Grandmamma is stubborn. Even after a life-threatening illness, and orders from her doctor not to smoke cigars, she continues to smoke for the rest of the story. This stubbornness, while bad for her health, translates into strength, which makes her cool under pressure – like when she talks down Mr Stringer from banning her grandson's pet mice (Chapter 5) or when she pretends she dropped her knitting when the Grand High Witch notices her on the balcony above her (Chapter 15). Even her young grandson is impressed: "I marvelled at the coolness of her voice" (15.17).
For all her strength and toughness, Grandmamma sure has a soft spot for her grandson, our narrator. Because this is a story about him, this is perhaps the part of her that matters the most.