Nightcore is a style of Electronic Music, in particular, a style of making music remixes where the song's pitch is altered (often to a major key) and the track is sped up to double the original BPM. Beats are made louder, and other edits are made, such as adding various digital effects, arpeggiated supersaw leads and eurobeat-esque backing melodies but the core element here is the speeding up. Basically a creative (ab)use of the Speedy Techno Remake, and user-made tracks are usually varied in quality, from well-composed, professional-sounding remixes to crappily sped-up songs with vocals that sound as if the singer had inhaled helium. There is also a unique type of Nightcore that is called switching vocals. There is 2 or more vocals mixed together with amazing effects. You can find many of these videos on YouTube (example video).
It's more of a phenomenon than a genre of its own, initially developing from the UK hardcore scene and branching out into other EDN genres from there. Most modern, well-made nightcore remixes fall under happy hardcore, UK hardcore, or eurobeat, though trance and even Drum and Bass-style remixes are not unheard of.
It has also become a catch-all term for any song that is sped up, which has become a source of Broken Base among fans of the style, as in such case, it's technically inaccurate simply speeding up a song without remixing it doesn't make it a "true" nightcore remix, with many YouTube content owners and practicing music producers calling out the uploaders on this (see below).
In terms of views, many nightcore remixes have more views than the traditional songs, but this doesn't necessarily mean the song has been Eclipsed by the Remix.
As time progressed, the term Nightcore has been widespread among various communities and groups, but for negative reasons. Music enthusiasts, artists, video game players, and music game players are the ones who hate this kind of phenomenon due to its usage in YouTube and its effortless and unethical monetization. Nightcore uploaders would rip music off of popular songs, use a free program such as Audacity to speed up the song and pitch, save an anime girl image off of Google and save the photo as a video, and upload to YouTube, calling it a remix or nightcore version, while often times not crediting the artist of both the music and the anime girl image. All at the same time, they would monetize the video. The process would take less than 5 minutes to do. With YouTube having heavier restrictions on copyrighted material (i.e. a music game tournament video getting flagged for having a sound sample of a song), its system does not exactly apply to material that has been sped and pitched up. It is indeed possible for some nightcore tracks to get more hits than the original track itself, upsetting the original artists and supporters. For searchers who want to hear a cover or remix version of a track, seeing nightcore labeled as a top search over actual remixers or composers is also insulting.