As I am in the process of creating my own music video, it makes sense that I should make a quick post about the purpose of music videos.
The key purpose of a music video is to help the artist/label sell their product. Using a music video to boost sales is very effective, especially now that the internet is used by the majority of people. The internet makes it very easy for the public to 'discover' new artists without really looking for them, mostly through the use of social networking sites and video hosting sites such as YouTube. If people find a video they like, they usually end up listening to more of the band/artist's music and eventually buying their album.
Promoting the artist is also a main purpose of music videos. For example, most music videos tend to have shots which are often separate from the main narrative of the music video, featuring close ups of the artist, allowing the audience to recognise them and 'put a face to the song'. Although it is a very shallow point, these close ups work especially well to promote the artist if they are shown to be attractive or desirable in some way, as attractive musicians (or 'musicians' in some cases) = hordes of fan-girls, who then post links to said artist so obsessively that it's virtually impossible for anyone NOT to have seen their music video. Relating back to the first point, promoting artists is much easier now that the internet is so widely used, as music videos can be seen and shared almost effortlessly.
Many bands and artists enjoy performing to an audience and creating meaningful music, so another reason they may create music videos is to entertain their fans, or 'bring to life' their lyrics by creating a video which explains them further. Personally I prefer music videos which leave the lyrics down to interpretation and do not force the audience to interpret them in a certain way, but many people like strongly narrative based videos, it's just down to preference really.