BitComet Support Team's BLOG

ASF stands for Advanced Systems Format. It was developed by Microsoft as part of the Windows Media framework. ASF is most commonly used for streaming media purposes. The format doesn't specify the way video or audio should be encoded. ASF specifies the structure of video or audio stream. Due to this encoded with different audio or video codecs the files will still have .asf extension (just like other container formats AVI or OGG).
Like ID3 tags for MP3 files ASF files can also contain objects representing metadata. For audio - artist, title, album and genre. For video - director. Files of ASF format support playback from digital media servers, HTTP servers, and local storage devices.

You can use mpcstar to open files with this suffix. http://www.mpcstar.com/