The original idea was to start with "roguelike" here, but unfortunately I'm not able to do that. The only roguelike that I spent a long time with is Angband (and I haven't even finished it once). However, show me something like Spelunky or Necrodancer or Risk of Rain and I'm guaranteed to spend a few evenings with it.
I'm not surprised if it's the first time you hear the term "roguelite" or "roguelike-like". I really think we should come up with a more approachable term for this basic idea. Let me explain it in one paragraph:
A roguelite is a game that you can finish in a few hours tops, but that you're not going to finish on your first attempt. It's a game where you're going to lose and then you're going to start over. However, losing is fun because playthroughs are short and expendable and you can quickly learn from your mistakes. Starting over is fun too because every single playthrough is going to be different: you will keep discovering new content and the challenges won't get close to repetitive for a good while.
Beating a roguelite is not just about playing it enough until you're done - it's more of an adventure where you progressively discover the challenges the game can throw at you and figure out a way to overcome them. It's an interactive learning experience, so the act of finishing the game actually feels like an accomplishment. This is a great improvement over classic games that are meant to be played A to Z, where reaching the ending resembles watching a movie or finishing a book - pleasant, but not "whoa I finally did it" pleasant.
I like that roguelites usually don't require a huge time investment in order to be fun. Hell, to the contrary - they're the most fun at the beginning because EVERYTHING is new and every consecutive run brings a ton of new content and depth. You don't have to give up a good portion of your life to enjoy a roguelite. You could just play for 30 minutes and have a great time, then come back when you feel like it! This is a healthy, non-addictive approach to player retention.
Roguelites come with little or no tutorials: you're expected and encouraged to learn by playing. I like this because I'm disappointed whenever a game has to explain things to me and I find pleasure in figuring things out. Great roguelites are optimised for discovery, so this comes naturally.
Some roguelites naturally generate great stories. Just look at this FTL review on Steam that greatly matches my experience from the game:
Shelton had in this time also suffered terribly - first fire, then half his health to suffocation - he left the Rockmen to deal with the flames and crawled back to his controls, and it was then he realised that in all the frantic action, and with the ship 2 bars to oblivion, his prized drones were still up and running! The words hull critical flashed over and over through his screen, but he took several deep breaths.. and waited.
The Roguelite is the endgame of gaming.