Dark Horse Comics began in Oregon as a publishing house that catered more to the creatives than Marvel or DC. This was in the same vein as what happened with Image Comics a little later on, with creatives trying to find more ways to use their own voice versus a corporate voice. The difference with Dark Horse as opposed to Image was that Dark Horse was a "corporate" entity, not owned by the comic book artists and writers like Image.
Dark Horse is not known for super hero comics, although they have had a few. Their top book ever was Frank Miller's Sin City. They also tend to make the books associated with films. Where Marvel and DC make films based off the books, Dark Horse buys the rights to make the film into a book.