A performance music video includes part or all of the band / individual performing the song the whole time. This can take place on a stage, or in a room on their own where it is clear no audience is involved.
This originated from rock bands who included performance in nearly all of their videos in the early days of music videos, rather than other genres of music.
An example of this is Nirvana - Smells like teen spirit
A concept video is where the video has no relation to the lyrics and no performance. Concept often includes either the vocalist in the band whose video is being produced, or a completely unknown figure.
Concept videos are often though of to be quirky and often 'wierd' for example The Pixies - Velouria is just a video of the band running over some rocks for 30 seconds, which then gets edited and slowed down to cover the whole of the song.
A narrative video is a video that follows the lyrics of the song with what is happening in the video. For example Smash Mouth - All Star include narrative by the main protagonist running into a house in a fire to rescue someone, but it also has the lyrics 'with an L on her forhead' as shown in the video.
These three types of music videos are often linked in the same video, for example a narrative video at one section could then cut into a performance of the band, which could then cut back to a concept idea involving the main protagonist.