Undertale imitates 80s console and PC hardware by using low-resolution graphics, monospace fonts, and chiptunes (music primarily made of square, triangle, and sawtooth waves).
Sprites in Undertale are rarely shown at their actual resolution. That is to say, the pixels composing any sprite are larger than the pixels on your screen. In this way, sprites imitate low resolution graphics (bigger pixels = fewer pixels). However, Undertale manipulates its sprites in terms of screen resolution.
There are two resolutions: one observed by the sprite artwork (few large pixels) and one observed by your screen (many small pixels).
For example, watch Froggit's head as it bobs. It will move in increments smaller than the pixels on its sprite. This is because Froggit's head moves in terms of screen resolution, not sprite resolution. Sprites also rotate according to the screen resolution.
This allows sprites to be more expressive than their low resolution art. In the 80s PC RPGs that Undertale imitates, sprites could only move in increments dictated by their low screen resolution. Undertale's art is drawn by that low resolution, but moves in a finer degree.
Undertale references a low-resolution format and performs actions that would be impossible at that low resolution. The Flowey boss fight, on the other hand, breaks the mold entirely. No portion of his graphics appeals to 80s standards.
Undertale's font also references 80s computers and consoles, featuring a monospace font. When Flowey says "Idiot," it is shocking in part because his font breaks this standard. The monospace font sets up an expectation of a simple retro RPG, and his new font breaks that expectation. Appropriate, since this is the moment that Flowey turns from friendly tutorial to would-be murderer.
Later, Sans and Papyrus also defy the font standard. This effect is fun, since we can relate their spoken font to their names. There is no definitive effect on the player beyond this. (If I claimed that this says something about their characters, I would be out on a limb.)
The music often blends chiptune with higher quality instruments, as well. The opening cutscene (climbing and falling in the mountain) contains only standard chiptune instruments, fitting with its setup as just another old-school RPG. After this cutscene, the soundtrack brings in higher quality instruments. The blend is loose, since tracks can have any range of chiptune and regular instrumentation. Even if a track is largely square and triangle waves, it will often have high quality percussion, such as the intro to the regular battle theme.
Undertale's aesthetic approach complements its critique of old JRPGs. Its aesthetics start with an inspiration in 80s hardware, be it graphical or audio limitations. Undertale then deviates on top of that, either manipulating sprites or using instruments in a way that 80s hardware could not.
