Discworld is a series of books written by Terry Pratchett (I believe there approx 29 of them at the moment).
They are a kind of fantasy humor set in a place called Discworld , which is a disc that rotates on the back of 4 elephants that is carried through space on a giant turtle.
The books revolve around many different characters and don't really follow on as such, just approx 29 stories set in the same world with many cameos of people from other books.
Very funny and highly recommended.
Death as the name implies is literally Death, The Grim Reaper who rides a great white horse called Binky.
A great character and the Skellington reference is from the book 'Mort' if I remember correctly, which is what a little girl calls him.
As for the Monkey thing, it is just a joke from work where we all call each other names that included the word-Slack
i.e Slack Monkey. Slack meaning lazy, and monkey meaning lower than a homo sapien.