Roguelike
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 (you can do lots of things in them, though the level of detail varies from game to game), high difficulty, lack of plot, permanent death, and randomization of content. Basically, expect lots of tactical options and such, though Crawl is more condensed than some others.
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Definition
Roguelikes, at their core, are games with permanent death and relevant randomly generated content. Crawl autosaves often, so once you die, you die, barring cheat options like explore mode. While you'll encounter the same types of monsters in similar locations, where and when are incredibly relevant details. What items you get, what gods appear early enough, even which branches appear, are random. The dungeon is for the most part randomly generated, and even the non-random vault is randomly placed (or may not appear at all). While not a strict requirement, Crawl follows the grand tradition of roguelikes by being a top down, tile based, turn based... dungeon crawller.
Difficulty
Roguelikes are not easy. 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. Oh, and if you die, the game erases your save file. Have fun starting over.
Non-existent plot
With a few exceptions (such as ADOM), a 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? Well, in NetHack, you want to get the Amulet for your god. In Crawl, you want the Orb of Zot for no defined reason. Xom could tell you, but then it'd have to kill you.
Randomization
A good deal of what keeps the game entertaining. Dungeons are randomly generated every time, with only a few things you can count on. Your item selection, stats, gear, monsters you run into and so forth will be at least somewhat different every time, which makes the game addictive rather than repetitive and tiresome.
Dungeon Crawl compared to other roguelikes
Crawl seems easier, at first glance, but it's not. It is, however, friendlier. There are no 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. Stone Soup not only has a tutorial and in depth manual, but provides extensive information of any monster, item, or other noun you may come across; all accessible by right clicking them (x then v via keyboard controls). The goal is that, unlike the older roguelikes, Stone Soup should be playable without the aid of a guide or wiki.
The DevTeam of Dungeon Crawl Stone Soup aims to remove 'tedious' mechanics from the game. Players in NetHack are heavily encouraged to go through Sokoban every game, a puzzle branch with 8 fixed layouts. With solutions easily available outside the game, the branch gives 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 0.24. Meanwhile, food was continously simpfied and eventually removed entirely for being a GUI hassle. DCSS also tries to remove 'no-brainers', or completely dominant items/strategies, for the same reason, even though balance is not perfect. On the other hand, Stone Soup is famous for its countless removals, regardless of how beloved a feature is.
Compared to other classical roguelikes, 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, also picked during the game (mostly). 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.