Files with .BIK extensions are BINK movies.
BINK movies are not specific to The Witcher; you can find it in several modern games. Undoubtedly however, the best quality BINK videos I've seen to date are those in The Witcher. The movies were created by Tomasz Bagiński, known for his Academy-Award nominated short animation The Cathedral.
BINK videos can be created and played back using the Rad Game Tools - meaning that if you download and install the RAD Game Tools (which is free), you can watch any BINK video simply by double-clicking on it.