Undertale works in large part because it follows a very simple premise and executes it with precision. You have an array of goofy, loveable monsters and you befriend each of them. This sounds rudimentary, but the skill with which it is done puts almost every "waifu" intensive game from Japan to shame. The final battle is, quite literally, in simplest terms, the power of friendship. And it works. You do not even notice it at the time because that is how undeniably charming these characters are. (One who is better read than me could probably go back to some of Tolkein's essays regarding the concept of the 'eucatastrophe' with regards to fairy stories and probably have something clever and insightful to say about Undertale's finale. I am illiterate and thus cannot say anything profound on the matter.)
In fact, the entire thing is pretty emotionally manipulative in that regard, but, to be fair, I am perfectly fine with this level of emotional manipulation in my games. Do it this well and you can prey upon my emotions like the most cruel predator. Once again, skill in execution can make the base and the basic delightful.
This focus on befriending goofballs is also helped by the pitfalls the game skillfully avoids. The backdrop speaks of a war of humans and monsters that the monsters handily lost, but no time is wasted subjecting us to tedious moaning about the cruelty of the humans or the victimization of the monsters. In addition, Undertale deftly sidesteps so many indie pitfalls. The game owes a lot, tonally speaking, to Earthbound but thankfully avoids retreading any of Earthbound's story beats, particularly the almost viciously trippy final battle. The obligatory creepy segment of the game avoids wallowing in schlock juxtaposition of cute and horror and stays in the game just long enough to be effective and is written into the universe in an appropriate manner (This was a pleasant surprise as I was so certain the game would jump the shark at that level.). In addition, without spoiling anything specific, Undertale plays games with the gamey aspects. Saving, reloading, and starting over are acknowledged in the game universe. In the hands of any number of indie developers (And a few professional developers, see Kojima, H.), this could easily have ended up spiraling the story off into an inescapable tail-spin of self-indulgent tangents and failed attempts at saying something profound. Undertale treats this fourth wall abuse with the respect it deserves: As a parlor trick. Deployed deftly to shake your expectations but impacting the plot only on the periphery. A subordinate priority to the main goal: telling a satisfying yarn and entertaining the customers.
That is another part of Undertale's success. It operates on multiple levels competently. The main plot stands on its own, bolstered by the metaplots, with a few mysteries hidden in the game code for the rumor mongers to chase. Every taste is catered to here.
Even the gameplay is effective. The combat is delightful, light RPG trappings cover the main gameplay: a pseudo shmup dodging system where each attack from an enemy challenges you to maneuver a heart through their attack pattern. The patterns are as diverse as the enemies themselves and reflective of their unique personalities in a way that even Touhou fails to accomplish reliably. The result is something that manages to be both fun and charming. Unlike so many other RPGs, the gameplay does not overstay its welcome, with the possible exception of repeat plays. The puzzles are usually quite easy, but woven into the story in a way that they far more effectively act as vehicles to showcase the characters. I should not spoil it but you will not get three rooms into Undertale without realizing exactly what this game uses puzzles for.
The weaknesses of the game are few. The idea of granting the player freedom to kill any character he wishes while at the same time spending all your energy to make every single character likeable and charming are design decisions at cross purposes. The ending text varies greatly depending on which of the principal characters you kill but, there is only one genuine threat to the player's well-being amidst all those characters. You would have to be cruel to make a choice to kill them and the game is a hair too long to do so just to make a run through to see a specific ending. Since the true ending requires a pacifist play through (After a normal playthrough, but if you were pacifist in your normal play through, you could just reload into that completed game and get the true end right away.), you may as well avoid unnecessary replays and do it properly. There are plenty of games where you can go out of character and murder people who do not deserve it but never so in a game with nearly aspect of these characters massaged and designed to be loveable and unthreatening.
To be fair, the game acknowledges this to a degree. A genocide run, an incredibly tedious and unpleasant affair, changes the story considerably, presenting your character as the sort of silent, unstoppable evil that unnerves people just by staring at them.
I would quibble with storytelling choices: The principle couples in the game are, in the order you meet them, lesbians, gays, and then a broken up heterosexual couple met only at the end, with the man in that relationship derided in almost cruel terms as feckless and impotent in a story context that makes little sense. Nothing in the game hangs on these relationships or focuses on them unduely (Just as we are spared bemoaning the cruelty of the humans.) but, at the same time, the message is plain as the nose on your face. Not a flaw of serious measure, of course, but one I must make note of.
Finally, as much as I love the ending, as well-executed as it is, there is not anything profound in it. Compared to Danganronpa 1 or Ghost Trick, whose climaxes posed challenges almost spiritual in nature (for the latter game, figuratively and literally.) or Ace Attorney 1's villainous plot whose cruelty was so perfectly symbolic as to be nearly a work of art, or Persona 4's social links and character interactions, addressing truly human questions that will stand the test of time as long as young men and young women go to school, even when posed from strange barbaric lands where school takes place on Saturdays and everyone calls everyone else san, kun, or senpai. Next to those greats, as much as I loved Undertale, I do not know if it can stand the test of time. The saccharine sweetness feels almost like something unique to the sort of generations where My Little Pony and magical girl anime can capture the hearts of men... I am not clever enough to make a real observation of how long it might last beyond mere feelings, but... note what I am comparing it to. That truly is praising with faint damnation, is it not?
tl;dr Play Undertale.