Discworld is a very long-running series by Sir Terry Pratchett (30 years!), which, as Admin said, take place on the back of the titular Discworld, which spins on the backs of four elephants who, in turn, stand on the back of the Great A'Tuin, who is a giant turtle.

The books don't follow any specific character, although there are sub-series which fall into certain genres and focus on certain characters or character groups.

The Watch books are about the City Watch in Ankh-Morpork, which is the biggest city (and, more correctly, it's a city-state) on the Disc, with an emphasis on Samuel Vimes, Captain and later Commander of the Watch.

The wizards books initially focus solely on Rincewind, who is a rather abysmal wizard and highly accomplished coward, but later they expand to include the rest of the staff of the Unseen University–Archchancellor Ridcully, the Dean, the Chair of Indefinite Studies, the Lecturer in Recent Runes, the Librarian (who is an orangutang), and Ponder Stibbons, although Rincewind is often still the primary character. These also frequently feature Cohen the Barbarian–who's in his eighties.

The witches books take place in Lancre, and follow Granny Weatherwax, Gytha Ogg, and whatever hapless new witch fills out the third member of their coven (Magrat Garlick initially, later Agnes Nitt/Perdita). At one point they leave Lancre and go to Genua.

A subset of the witches books are the Tiffany Aching books, which are aimed more at young adults and which follow the eponymous character. (And the reason they are YA and not "adult" is that Tiffany is... nine...? in the first book. Instead of an adult. That is literally the only difference between adult/YA books in the Discworld series. Which is to say that even the adult books are pretty PG [in the same sense that Doctor Who is PG])

The Death books focus on the Anthromorphic Personification himself, his companion the Death of Rats, his manservant Albert, and his granddaughter Susan. Despite his job, he's one of the kindest, most honest characters on the Disc–albeit occasionally misguided. 

The most recent sub-series, the Moist books, follow the life of Moist von Lipwig, a fast-talking and highly inventive conman-turned Postmaster General-turned banker.

There are also several standalone books scattered throughout the series, some of which examine other regions of the Disc–Klatch, Borogravia, etc. Others take place in Ankh-Morpork.

It's a phenomenal series with well-written characters and quality plots. Guards! Guards!, Hogfather, and The Truth are all good places to start. If you want to start at the beginning (which, it should be noted, is NOT necessary), The Color of Magic and The Light Fantastic are the first two books and tell one story between the two of them.

And, obligatory fangirl time: squueeeeeee Discworld is the best series everrr!!!!!11!1 

TOP

TNO explained it well. But I'm not a big fan of them. I read Feet of Clay but quit halfway. They're boring and a bit confusing but I also think Hitchhiker's Guide to the Galaxy is boring. So if you like HG2G then you'll probably like DW.

Only thing to add is SQUEEEEEEEEEEEEE!!!!