It’s a computer game series of mostly danmaku shooters (stuff where you control a plane/ship/character and have enemies scrolling onto the screen shooting at you, like Gradius or Galaga, but with an emphasis on intricate bullet patterns). The games are all made mostly by one guy in Japan.
The games have a huge cast of characters (each game can have close to a dozen or so characters, and a lot of them are original to the game they appear in, so it adds up) based largely around Japanese mythology. The characters and the music are probably the two most famous aspects of the game.
Here is an example of a stage from one of the games on its toughest difficulty setting:
There are also a few official fighting games made in collaboration with another group of game designers, plus some official media (books, manga, etc). In addition, there is a huge amount of fan-made works, including doujin games, fanart, fiction/manga/animated videos, musical arrangements, etc, and a lot of it is professional quality. Because of all the material outside the official games, there is a pretty big fandom outside of the games as well.
The picture above is a fanart of the series’ two main protagonists.
I’ve been playing Imperishable Night more lately. I’m doing better with that than EoSD, but I still can’t 1 credit clear Normal. I was playing through on Easy for fun, though, and was surprised to find you can actually unlock the Extra stage on Easy in that game.