Traditional skis and boards had camber. This is like a spring built into the profile that spreads your weight through the length of the ski or board. How stiff the spring is will determine the performance of the ski or board. When you are standing on the ski or board your weight flattens the camber, the part of the base that is touching the snow is the contact point.
There are very few ski's and boards now that have only camber. You will usually find full camber on racing ski's and some freestyle skis and boards as camber gives more "pop" off the jumps.
Most modern skis and boards have rocker in some form. The first method is tip rocker. The tips start rising up earlier which makes the contact point smaller. This makes it feel like you are using a smaller ski or board, which you are as there is less in contact with the snow. Tip rocker also helps with turn initiation. You turn by putting the ski or board on its edge and bending it. Rocker is like pre bending the ski or board, making turning easier.
Tip rocker is often found on ski's and boards intended for use mostly on piste.
Tip and tail rocker is often found on ski's and boards intended to be used all over the mountain. Rocker reduces the contact point without reducing surface area, so on-piste they feel shorter, but if you go off piste there is more surface area to keep you on top of the snow. Rocker in the tail helps to finish the turn as its is pre-bent, this gives you extra maneuverability through the varied conditions off-piste.
In snowboards there is another version of this, Nitro call it Gullwing. This has camber under the bindings and rocker between them and in the tips and tails. On firm snow this gives the feel of a camber board and off piste the feel of a flat or full rocker board.
No camber makes a very playful ski or board, they are very easy to turn and spin.You will often find a flat profile on a freestyle ski or board. They are easy to use so if you are a beginner they are pretty forgiving.
Also know as reverse camber or banana, full rocker is intended for powder. Go off piste, in the back-country or heli-skiing. In soft snow off piste its hard to bend the ski or board to turn as there is little resistance pushing back. A full rocker profile is already bent which is what helps you turn. On firm snow there is a very little contact point so don't expect a lot of grip.
Rocker and the effect on size
So when trying to decide what size to get remember to factor in the rocker profile, the more rocker it has, the smaller the contact point is, the bigger size you will need.
The Armada JJ in the example below is a great example of how rocker effects the choice of ski size. The widest point of the ski is set back where the rocker starts. This gives the 195cm ski a smaller contact point (the red lines) than a 144cm Dynastar Women's piste ski (the blue lines).