One-shot manga usually only consist of one chapter, so what is their purpose? Is it mainly for promotion, filler or contest? And do they have their own media (like a magazine that only consists of one-shot or something)?
Manga magazines usually have many series running concurrently with approximately 20–40 pages allocated to each series per issue. Other magazines such as the anime fandom magazine Newtype featured single chapters within their monthly periodicals. Other magazines like Nakayoshi feature many stories written by many different artists; these magazines, or "anthology magazines", as they are also known (colloquially "phone books"), are usually printed on low-quality newsprint and can be anywhere from 200 to more than 850 pages thick. Manga magazines also contain one-shot comics and various four-panel yonkoma (equivalent to comic strips). Manga series can run for many years if they are successful. Manga artists sometimes start out with a few "one-shot" manga projects just to try to get their name out. If these are successful and receive good reviews, they are continued. Magazines often have a short life.
One-shot manga tells its entire story in 15-60 pages, usually written for contests, and sometimes later developed into a full-length manga series (much like a television pilot). Many popular manga series began as one-shot stories, including Dragon Ball, Fist of the North Star, Naruto, Bleach, One Piece, Berserk, Kinnikuman and Death Note, among others. Some noted manga authors, such as Akira Toriyama and Rumiko Takahashi, have worked on numerous one-shot stories in addition to their serialized works. Rising Stars of Manga was an annual competition for original English-language one-shot manga, many of which have gone on to become full-length manga series.
Note: Emphasis mine.
A lot of larger series start off as one-shots - like Naruto, Death Note & Dragon Ball. In this case, it's similar to pilot episodes of TV Shows which are used to test the waters before expanding the story out any more.
Oneshots can be for more than the viewers, and can be created to give publishers a feel of what they'd be getting.
Mangakas often use them also to experiment with a story or art-style without having to be tied down with it for several chapters.
Oneshots are also often used for manga competitions, such as TOKYOPOP's Rising Stars of Manga