Files with .BIK extensions are BINK movies.
BINK movies are not specific to The Witcher; they are found in many modern games. Undoubtedly however, the best quality BINK videos I have 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 are free), you can watch any BINK video simply by double-clicking on it.