I grew up with them so take my glowing reviews with a pinch of salt.
The books are a wonderful take on humans. The discworld has a broad theme that stories are real and powerful in the same way humans often believe them to be. The way we see and talk about the world is how reality works there. So cold is more than the absence of heat, there are deafening silences that drown out sound and gods are formed by and from belief. Many more things but those would often give away part of a discovery that's best found while reading.
The characters range from fun to deep, and feel consistent.
Apart from the first two or three books being quite different, there's a solid consistency and branching and merging set of storylines across 30+ books.
Also there are many references to our world and/or puns that I slowly realise and get now I'm in my 30s. They feel like they contain just so much.
They're not a chore or a slog that's "worth it in the end" and there are various places you can just jump in.
Sir Pterry was a proper old school journalist and writer. He was incredibly well read and was meticulous in his research. Oh and he wrote some books! He had a facility with language that was often breathtaking and an understanding of people and relationships that is easily relatable.
He chose the medium of fantasy and really ran with it. After the first two Discworld novels he really got into his stride and would generally pick on a theme per book and really go to town on it. Who else could turn stamp collecting ("Going Postal") into a real page turner?
You get characters like the Patrician (a sort of medieval Italian city state despot crossed with ... well he's unique and can thrash a cryptic crossword and has an elderly dog) and Sam Vimes (from guttersnipe to Lord in a very complicated lifetime). You get real witches and wizards (some of who end up playing football - soz soccer). You get the memorable Granny Weatherwax and ... and. Basically you get loads of beautifully crafted and rendered characters. Oh and you get Gods and Death too (he rides a horse called Binky)
Pratchett has been accused of Literature and it would probably stick if his works were not so enjoyable and accessible to read. He has been translated into a lot of languages which implies to me that his world view really is that - a world view that is worth investigating.
That Sir Terry had a facility with language is true. It also does no justice to that aspect of his writing.
How could anyone with half an imagination read something like "Octarine ... the undisputed pigment of the imagination" and not laugh? I'm not even going to mention the reflected-sound-of-underground-spirits, or Cohen the Barbarian, or the many names of Bloody Stupid Johnson.
I find it marginally painful that someone is hesitant to try reading a new (to them) author. If one turns away from Pratchett in hesitation, what fate might befall Chinua Achebe, or Ryszard Kapuscinski, say? I wonder if it says something about the kind and quantity of pretentious garbage (literary, cinematic, political, and otherwise) that surrounds us and pervades almost all aspects of our lives - so much so that we are afraid of spending a little time reading a book that we might not like?
Satire/comedy helps me cope with the world. For me, his stories are a nice balance of story, pragmatism, stoicism, fantasy, whimsy, and most of all satire. I particularly love his dialog. I have been searching (in vain) for whimsical/clean satire that helps me cope since Pratchett’s passing.
I second the suggestion to give one a go. Pratchett is not for everyone though. I encouraged my office mate to read Going Postal; he liked it so so, but declined to read another. My flight instructor liked small gods at first, but then didn’t; he wanted to dissect it too literally. I think it bothered him that it didn’t validate his view point as an atheist, instead flirting with many of Pratchett’s common satire of organized religions. My son loved every Sam Vimes book, but didn’t care as much for the others. A good friend tried one, was ok with it, and then read Hogfather, after which he said “give me every one of these that has Death in it.” My daughters really enjoyed Tiffany Aching, I had read Maskerade earlier to them, but only when they did finish Tiffany Aching did they really want more of the witches. My opera trained daughter now counts Maskerade as one of her favorites. As others have pointed out, his earlier works are more whimsical (think Monty Python or Hitchhikers Guide). Near the end of his life, Raising Steam was sadly predictable in its plot as a “tying things up” song. Me personally, I didn’t care for the Rincewind novels, until I watched one of the BBC adaptations, the one with Jeremy Irons, and now I even like the Rincewind/Twoflower/Cohan books. My wife thinks they are all eye rollingly silly and wonders why we get so excited about them.
Which is meant to be a long winded way of illustrating that you may have to poke around a little to find the satire and/or personalities that really resonate with you.
If you’re looking for something that has the closest connection with programmer geek culture, then I suspect Going Postal with its satire on who controls the flow of information (e.g. the web), it’s “code shifters” and the “Smoking GNU”.
I'd suggest to make the small one-time investment of purchasing "Wyrd Sisters" to find out for ourself. If you like it, keep going as it gets better. If you don't like the style, the other books are not going to change your mind.
I started reading his books from the start again a few weeks ago after about 15 years of a break. The first few books aren't great because it feels like he hasn't quite decided yet what to do with the whole Discworld thing. The one mentioned above is the first where it feels coherent and his wit and craftsmanship with words come out. You are not missing any meaningful context by skipping the ones before.
The biggest thing to be hesitant about is how many of them there are, so if you want to collect them you'll have to invest in extra bookshelves. The "reading order" charts can also be daunting (though it mostly doesn't matter).