The "Hogfather" of the title is the Discworld equivalent of Santa Claus, and this book centres around the fictional Discworld tradition of Hogswatchnight, basically their version of Christmas.
However, close to the start of the book it becomes apparent that something is not right - instead of the Hogfather showing up at peoples' houses, Death starts dressing up in a red cloak and delivering presents, standing in for the Hogfather, who is apparently dead.
Meanwhile, a unseen university a bizarre series of events starts when Archchancellor Ridcully decides he wants his own private bathroom because of the "verruca gnome" being very busy in the communal bathroom. Suddenly, the Verruca Gnome comes into existence, and it soon becomes apparent that anyone or anything who the wizards believe in immediately exists.
Amongst all this, Susan (previously seen in Soul Music has to track down a group led by the assassin Teatime, who are pursuing the Tooth Fairy.
Most of the big laughs come from the scenes with the wizards, and in particular Death's attempts at understanding the meaning of Hogswatch, which include giving away items in a department store where he is working to children. My favourite scene in the book is this one:
In the grotto of the Hogfather, a round-eyed child.
HAPPY HOGSWATCH. HO. HO. HO.AND YOUR NAME IS ... EUPHRASIA GOAT, CORRECT?
"Go on, dear, answer the nice man."
"'s"
AND YOU ARE SIX YEARS OLD.
"Go on, dear. They're all the same at this age, aren't they..."
"'s"
AND YOU WANT A PONY -
"'s". A small hand pulled the Hogfather's hood down to moth level. Uncle Heavy heard a ferocious whispering. Then the Hogfather leaned back.
YES, I KNOW. WHAT A NAUGHTY PIG IS WAS, INDEED.
His shape flickered for a moment, and then a hand went into the sack.
HERE IS A BRIDLE FOR YOUR PONY, AND A SADDLE, AND A RATHER STRANGE HARD HAT AND A PAIR OF THOSE TROUSERS THAT MAKE YOU LOOK AS THOUGH YOU HAVE A LARGE RABBIT IN EACH POCKET.
"But we can't have a pony, can we, Euffie, because we live on the third floor..."
OH, YES. IT'S IN THE KITCHEN.
"I'm sure you're making a little joke, Hogfather," said Mother, sharply.
HO. HO. YES. WHAT A JOLLY FAT MAN I AM. IN THE KITCHEN? WHAT A JOKE. DOLLIES AND SO ON WILL BE DELIVERED LATER AS PER YOUR LETTER.
"What do you say, "Euffie?"
"'nk you"
"'ere, you didn't really put a pony in their kitchen, did you?" said Heavy Uncle Albert as the line moved on.
DON'T BE FOOLISH ALBERT. I SAID THAT TO BE JOLLY.
Oh, right. Hah, for a minute-"
IT'S IN THE BEDROOM.
"Ah..."
MORE HYGEINIC
Susan's storyline proves to be somewhat darker, and Teatime is an effectively creepy villain, and it all leads up to a climactic scene in the Tooth Fairy's castle. The central message to this story is about how people like Santa Claus can only exist if people believe in them.
Most of the humour is satire directed at peoples' behaviour at Christmas, and just about every modern tradition is made fun of here, and there is some good social commentary from Death's very touching believe that everyone should be treated fairly at Christmas, while Albert has to explain that this doesn't exactly happen in the real world.
I noticed that the book also referenced various Christmas songs throughout in Terry Pratchett's usual witty style, and there are a few references to The Lion, the Witch and the Wardrobe, plus a computer that seems very similar to HAL from 2001: A Space Odyssey.
Overall, this is my favourite book in the Discworld series, and at its centre it feels like a festive and heartwarming tale.