Gran Hempstock is, how should we put this gently, umm… awesome. She's older than the moon, and yet she's still up for battle with devious hunger birds (after a nice restful nap, of course). She'd probably be able to knit a wonderfully retro wool sweater for us, but why waste her time when she can do things like make the full moon shine on a particular window every night?
Gran gives the impression that she knows everything there is to know, and there's not much reason to doubt her—after all, she was around for the creation of the world. Check out her take on bacteria:
"Mother!" she said. "Giving the boy honey. You'll rot his teeth."
Old Mrs. Hempstock shrugged. "I'll have a word with the wigglers in his mouth," she said. "Get them to leave his teeth alone."
"You can't just boss bacteria around like that," said the younger Mrs. Hempstock. "They don't like it."
"Stuff and silliness," said the old lady. "You leave wigglers alone and they'll be carrying on like anything. Show them who's boss and they can't do enough for you." (3.106)
We'll take her over amoxicillin any day, please and thank you. Also—this is one lady who clearly doesn't doubt herself.
In terms of where she fits into the novel, Gran is the character that can come to the rescue when everyone else is kinda lost. Her advanced age, experience, and unique perspective on the world allow her to see things that others might miss, or to know how to solve things when everyone else is totally flummoxed. Gran is the only one capable of "snipping" the bathtub incident from the boy's father's mind, and she's also the only one who can send the hunger birds packing with a speech like this:
"Shall I bind you creatures in the heart of a dark star, to feel your pain in a place where every fragment of a moment lasts a thousand years? Shall I invoke the compacts of Creation, and have you all removed from the list of created things, so there never will have been any hunger birds, and anything that wishes to traipse from world to world can do it with impunity?" (14.88)
Remember this the next time you whine about having dinner with your grandparents: Sometimes old people are cool because they know stuff.