Advanced Streaming Format. Microsoft's new audio/video format, meant specifically for streaming purposes. It doesn't specify how the video or audio should be encoded, but instead just specifies the structure of the video/audio stream. This means that ASF files can be encoded with basically any audio/video codec and would still be in ASF format.
Many times ASF is confused with Microsoft's implementation of MPEG-4 video format, because most of the ASF streams are encoded using this technology.
Links:
Latest VirtualDub to include ASF support
How to play ASF files