Simple Profile in this context is one of the video encoding layers available in MPEG-4 standard and is probably the most widely used.
Popular MPEG-4 codecs such as DivX and XviD use Simple Profile and also Advanced Simple Profile for video encoding.
Simple Profile is intended for use with low powered CPUs. As a result no B Frames are allowed. B frames, or Bidirectional-Predictive Encoded frames require two reference frames to be decoded, compared to the single reference Frame required for P frames. Since ASP isn't designed with this hardware limitation in mind it supports B frames.
Simple Profile is suited primarily for applications such as mobile phones and video conferencing where quality is less important than size. Video encoded to Simple Profile specifications is suitable for Muxing into a 3GP Container for use on a 3G mobile phone network.