A roguelike game is a type of role-playing game named after the genre defining Rogue. Features that are common to all Roguelikes include depth, permanent death, and randomization of content. Basically, expect lots of tactical and strategical options, though Crawl is more condensed than some others.
What is a Roguelike?
Roguelikes, at their core, are games with permanent death and randomly generated content.
Crawl autosaves often. So barring cheat options like explore mode, once you die, you die. Your save file is erased. Therefore, everything is a legitimate threat to some extent, and this only abates slightly at higher levels. Things can kill you if you're not careful, even things you wouldn't normally consider dangerous. And yes, you will often die in horrible, random, arbitrary ways. Have fun starting over. Roguelikes are not easy.
No Meta Progression
Crawl features 'true' permadeath. Nothing tangible carries over between games - you don't unlock new characters, items, or perks, and nothing from your past game influences your next game. Although player ghosts are based on previous games, they don't give any special loot. And in an online server, you're just as likely to find another player's ghost. Anyhow, a large selection of challenging ghosts exist even on a fresh install (from Stone Soup 0.22 onwards). The thing that gets better is you, the player, and perhaps a bit of luck.
Relevant Random Content
While you'll likely encounter the same types of monsters in similar locations, where, when, and if at all are incredibly relevant details. An ogre on D:3 is much scarier than the same ogre just two floors later. What items you get, what gods appear early enough, even which branches appear, are random. The dungeon layout is for the most part randomly generated, and even the non-random, handmade vaults are randomly placed (or may not appear at all). This hopefully makes a roguelike addictive, not repetitive or tiresome.
Grand Tradition of Roguelikes
While not a strict requirement, Crawl follows the grand tradition of roguelikes by being a top down, tile based, turn based... dungeon crawler, being what PCs during Rogue's creation could handle. This is in stark contrast to many more modern roguelikes (traditionally called roguelites), which have a wide variety of gameplay genres. Limitation breeds ingenuity, so while the format has some flaws (see pillar dancing, luring...), the ASCII gameplay loop is still exciting to play.
Most CRPGs, including most roguelikes, have roots from D&D's style of character creation. Characters in Crawl have AC, or armor class (though it reduces damage, while EV/evasion and SH/shield outright stop attacks), three attributes (STR, INT, DEX), and a host of high fantasy weapons and spells. Crawl is twice removed from D&D (taking inspiration from NetHack (Hack) -> Rogue -> D&D), but the similarities are still present.
Crawl also features 27 different species to play, which helps a lot with replayability. A Human might be the perfectly plain experience, but there's a wide variety of races: from Minotaurs and Trolls to gimmicky species like the 8-armed, 8-ringed, Octopode, who simply won't fit into most armour. Each species might be better with certain items, but the RNG could always favor something outside your plans.
With a few exceptions (such as ADOM), a classical roguelike's plot consists of the following: go down into a randomly generated dungeon, reach the final level, and either kill the boss or, more commonly, grab an item and escape. Why do this? Well, in NetHack, you want to get the Amulet for your god. In Crawl, you want the Orb of Zot for absolutely no defined reason. Xom could tell you, but then it'd have to kill you. Other than getting runes and the Orb, or unlocking treasure troves, there are no quests. Other than a shop (a glorified menu), there are no dedicated NPCs.
Dungeon Crawl compared to other roguelikes
Crawl (specifically, Stone Soup) defines itself from its contemporaries with a strong set of design philosophies.
Crawl seems easier, at first glance, but it's not. It is, however, friendlier. At least in DCSS, there are no real instadeaths. If something kills you, it'll probably be something you at least half-expected: an out-of-depth monster at an early level, rather than a necklace you put on happening to be an amulet of strangulation. The only non-HP related death as of 0.29 is the Zot clock, and that's only when you are reduced to below 10% of your natural maximum HP, and only after multiple, significantly long warnings.
Stone Soup not only has a tutorial and an in-depth manual, but provides extensive information of any monster, item, or other noun you may come across. You can access them all by right clicking their tile (or x then v with keyboard controls), or using ? / followed by what you want to search for. The goal is that, unlike other roguelikes, Stone Soup should be playable without the aid of a guide or wiki.
Crusade against Tedium
The DevTeam of Dungeon Crawl Stone Soup aims to remove 'tedious' mechanics from the game. For a player with knowledge of the game's spoilers, certain mechanics can serve to waste their time and energy. For example, players in NetHack (3.4.3) are heavily encouraged to go through Sokoban every game, a puzzle branch with 8 fixed layouts. With solutions easily available outside of the game, the branch gives good rewards: food that can last the entire game, along with helpful guaranteed end loot. Stone Soup has removed their own (completely random) puzzle branch, the Labyrinth, in 0.23. Meanwhile, food was continuously targeted, facing multiple simplifications and eventual removal. The Labyrinth could be solved with just a few rations, while food itself just became a clock that required opening a menu every few minutes.
In the same vein, DCSS also tries to remove 'no-brainers', or completely dominant items/strategies. Balance is not perfect, and not even intentional. For example, species is used as a difficulty slider: a Mummy is much harder to play than a Minotaur. Yet Crawl remains fairly balanced; a single player game has much more leeway with balance, after all.
On the other hand, Stone Soup is notorious for its countless removals - regardless of how beloved a feature is. The Mountain Dwarf was a seemingly benign species, but it was removed for being too similar to Hill Orc and Minotaur - all 3 were melee and armour focused races. While it would be easy to just not play MD, the DevTeam has decided that the 'fake choice' presented by too many similar species actually hurts the game, a.k.a that they detract from "every species feeling distinct or unique". Their removal, as the biggest example, has created a DevTeam and community accepting of dramatic change. But as a free and open source game, you could always play an old version, or one of Crawl's many variants (though sacrificing any future changes you may have enjoyed can still be disappointing).
Difference in Character Building
Compared to other classical roguelikes, and many CRPGs in general, Crawl places little importance on class (Crawl's backgrounds). There are no special, permanent rules for them. Skills, trained in game, are what really determine your character's specialties.
Gods are another character defining aspect of your character, also picked during the game (for the most part). Adventuring with one of 26 unique gods will earn you piety, with a large variety of special abilities and perks. Almost all gods will get angry if you leave them, so characters completing a regular game will most likely stick to just one.
- Wikipedia on Roguelike