Mike Stewart is not only the icon and innovator of bodyboarding but also has a fantastic ability to explain all the facets of the sport, from board design to how waves work, duck diving and maneuvers. Unfortunately his site is being revamped for 2008 so that info is not currently available. To answer your question until the site is up, read below:
(I coped this from and old mag of mine):
Measurements and how they affect the board's performance in the water.
Nose
The width of the nose affects the board's manoeuvrability.
A wider board (between 11 and 13 inches, better suited to prone riders) will be more stable, whereas a narrower one (anywhere from rounded to 10 inches, preferred by drop-kneers) will be looser and more manoeuvrable. Too wide and you will start to loose speed, too narrow and you'll have a hard time controlling your board.
Tail
Like with the nose, a narrower tail is easier to release for moves, whereas a wider one offers more stability.
As for different types of tails, they all work on the two principles - more edge for control (crescent) or more surface for drive (bat tails).
Wide Point
The widest point is taken from rail to rail across the board. It affects both floatation and and turning ability. A wider board will offer more floatation but will be harder to turn. Over the past few years boards have become narrower and narrower (most now under 22 inches) to accommodate for sharper and harder turns in more critical situations.
Nose to Wide Point
This is the distance from the nose to the board's widest point. It determines the board's overall shape and template. A higher wide point creates more surface area around the nose and offers more stability to the prone rider, because it's where you drive and manoeuvre from. Bringing it back increase manoeuvrability, and makes it more suited for dropkneers, as you pivot with your knee, not your elbow.
Rails
The amount of angle a rail is cut on affects the amount of edge it offers. A lower angle will provide more speed but less control, while a steeper angle increase bite (wave holding ability), but reduces the drive. 50/50 and 60/40 rail ratios are the most common because they offer a good balance of both, with a rail angle of between 30 and 35 degrees.
Channels
The principle behind channels is that they create additional turbulence, offering more 'grip' resulting in better wave holding but also making it slightly harder to release the rail for spins etc.
Core
There are 2 common types of core - Polypropylene (PP) and Polyethylene (PE). While there are many variations of cores, the basic principle stays the same. PP cores are stiffer and lighter than PE. They also tend to boast better response and flex properties which can aid in the control of the board (remember, the colder the water, the stiffer your board becomes and visa versa). Neither core is said to be better than the other, it's purely personal preference, what properties you like most in a board.
here's the link to Mike's site for when it is back up:
http://www.mikestewart.com/
Another comprehensive description can be found on Alistair Taylor's website
http://www.altaylordesigns.co.za/boards/index.php?option=com_content&task=view&id=14&Itemid=28