Mod16 simply means that the horizontal and vertical resolution of a video can be divided by 16, with no remainder.
For example, a video with 640x480 resolution is considered to be mod16, as 640 divided by 16 is 40 and 480 divided by 16 is 30.
This is an important rule because most video formats divide images into blocks of 16x16 resolution before encoding the blocks. This is especially important in MP4 videos, which are the format of choice for iTunes and others.
If the video is not mod16, data will extend outside of the blocks and the video codec will have to fill the data, thus reducing the quality of the rest of the encode.
You may have noticed Blu-ray players and other devices struggle with non-mod16 resolutions, sometimes running green strips along the side or tops.