A few things make it popular, in my own opinion/view, starting with the actual gameplay element as #1:
1. It's an RPG that genuinely is DIFFERENT. It's not another JRPG wannabe, and it's not another Skyrim clone. Even in combat, you dont play it like pretty much anything else. When enemies attack, your cursor... representing your character... is shifted into a box (you cant go out of it's boundaries) and enemies fire bullet-hell type attacks at you, which you must then dodge. They keep doing this for a time, until their turn ends, at which point you can then select an action before the next round of flying pain comes at you. But it goes further than that, by frequently bending it's own core mechanic in unusual directions. There's one character that can actually KEEP attacking you when it's your turn to select an action; your cursor is acting, in fact, as a cursor, jumping from one option to the next as you go to select things and move it around, but it can still take damage because the guy doesnt relent. The attack is specifically formatted for this (you'd have to see it to understand what I mean). And the game switches it up a bunch. There's a couple of fights where the bullet-hell aspect is combined with what is essentially "platforming" attacks, where there's suddenly gravity, and you have to "jump" to avoid tall bullet walls that come horizontally at you. It likes to throw in twists like this to keep things fun and interesting.
2. That's just the gameplay differences; there's other conceptual differences too. It's labeled as "The RPG where nobody has to die", meaning, you can literally go through the game while killing nothing at all. You can go through and win each fight without ever actually using the attack command (you will never get EXP this way though, but you dont actually NEED that... I wont spoil that bit though). You get a "Mercy" command that you can use, but it's not so simple as just clicking it and the fight ends; there's always more to it, depending on the enemy (it varies from one to the next, as to what you have to do) and you still have to deal with dodging their attacks, as they wont stop doing that on their turns until the fight has ended one way or another. Even bosses have this; the other label the game likes to put forth is that it's the game where you can befriend all of the bosses. Which is true. Bosses in particular also tend to keep talking to you during fights, you tend to sort of "meet" the characters in this fashion.
3. You do though have the OPTION to kill things. Once something/someone is dead, they're gone forever. They dont like, magically come back later because some pre-set cutscene dictates that they must. They're just plain GONE. Playing the whole game this way is called the Genocide route, and leads to an entirely different final boss and ending; there are various bosses and endings to get. Even the game's atmosphere changes depending on this; if you're in a run where you're not killing anything (or mostly not killing) the game will tend to be bright and hilarious. But if you've been murdering everything... it'll take on a darker, more somber nature, as characters grow to hate you more and more for the threat you've become, wanting to stop you from hurting anyone else. At that point, you the player are the villain, with the others seeking to defend their world and friends from you. It is of course more complicated than JUST that though, but again, not going to spoil it.
4. The characters are really memorable. This is a rare trait, it doesnt happen often in games. Frankly, most games cant do it. It's very, very hard to create truly memorable characters that essentially become icons of the genre or whatever. But it's really just impossible to not like these guys. Cant explain this bit any better than that... it's the sort of thing you have to see for yourself.