Kneeboards are made from 2 main materials - rotomolded plastic or composite material (a bit like a wakeboard). Rotomolded kneeboards are perfect for recreational / family use as they offer fantastic value for money and are extremely robust. Composite kneeboards offer higher performance but are more expensive and fragile. If you are new to kneeboarding or are looking for a family board then a rotomolded board will be perfect for you.
All kneeboards have a soft foam knee pad for you to basically kneel in and the foam is there to take a lot of the shock out of the ride and soften any harsh bumps. A strong webbing and velcro knee strap is also included with most kneeboards, which enables you to attach yourself securely to the board but in such a way that the strap will release in a tumble.
Recreational / beginner kneeboards often have what is known as a Hydro Hook (a.k.a. Aquatic Hook). This is a simple plastic flip-up hook (or plastic block) attached to the nose of the board to enable the tow handle to be attached to it and take all the load during deep water starts. The handle is simply placed behind the hook, which then takes all of the load off the rider when the tow vehicle powers up. Once up to speed and composed, the rider can then pull the handle toward them, which detatches it and gives them full control.
Rocker is the measure of how much a Kneeboard curves from nose to tail (kneeboards are somewhat banana shaped when viewed side-on). The higher the number the greater the curvature. Recreational boards are designed with quite a lot of rocker as this makes them slower in the water, more forgiving, and more relaxed in the turns. They also provide softer landings if/when you get "air". Intermediate and advanced boards have less rocker and are therefore faster in the water and in the turns, but landings will be harsher as a result.
Beginner / recreational kneeboards have soft rounded edges whereas intermediate to advanced boards have quite sharp ones. Rounded edges make the board less agressive in the turns and are better for beginners as you are less likely to "catch an edge" and take a tumble.
Fins provide forward stability and tracking and give the kneeboard "grip" on the water. Without fins a kneeboard will still travel in a reasonably straight line as it is longer than it is wide, but it will be able to rotate freely and very loosely on the surface of the water which requires skill to control. In addition to straight line tracking, fins also enable the rider to load up the line and accelerate on the approach to the boat wake. They then provide grip and stability on the landing. Kneeboard fins are normally moulded into the board along with moulded channels for additional stability and grip. The nearer the edge the fins are the more effect they have and the bigger and wider they are the more drag they create and therefore the more stability they provide. Beginner kneeboards therefore tend to have larger wider fins and advanced boards have smaller thinner fins (or none at all). Some kneeboards also have retractable fins so that beginners can get the benefit of the stability they provide but more advanced riders can retract them and obtain the more desirable "loose" feel necessary for performing tricks etc.