Two-pass encoding is based on some fundamental principles of digital encoding...
Rather than just tell you "it encodes better", the actual "how" and "why" is something like this...
The fundamentals of digital encoding, whether video, audio or any other sampling for reproduction purposes dictates that the most critical component in digital-to-analog or analog-to-digital conversion is a sample and hold buffer.
The shorter duration a value is held in memory, the greater opportunity for sampling and quantization error. In the case of professional DVD encoding, DVD Forum guidelines recommend two-pass variable bit rate encoding.
In the case of using something like Handbrake for encoding to a format readable by iPhone, you're using a constant bit rate (CBR), but the two-pass method reads the values once for initial encoding, and then again for sampling error correction. In scenes involving considerable change in values... e.g. lots of action which means lots of pixel value changes in a short amount of time, the two-pass method is going to result in a much more accurate reproduction of the original because the encoder gave each value a second sampling to compare against the first and fix any errors that would otherwise remain in a one-pass encode.
