In order for the electrolysis to work, both electrodes need to be in contact with the electrolyte.
I think what Cesium meant was that you should position the electrode so that it is just barely touching the water, so that very little of the electrolde material is submerged. By doing this, any Cl2 bubbles which form, form very near the surface and do not have much of an opportunity to dissolve in the water, they reach the surface and [hopefully] blow away. By contrast, if you submerged all of the electrode, the bubbles of Chlorine gas formed would need to travel all the way up through the solution in order to get to the surface, all the time, a little bit of Chlorine goes into solution.
However, with most[/all] electrode materials, current density is very important, especially on the anode.
Some materials (graphite is a great example) will erode away when used as an anode in an electrolytic cell. In order to slow this erosion process, it is a good idea to keep the "current density" (the current per unit surface area) as low as possible. By only submerging the end of the electrode, you are forcing a very high current denisty and the electrode will likely erode away much quicker than if you were to submerge the entire length.
This process of anode erosion becomes particular important when dealing with cells which need to be run for long periods of time (Chlorate cells) and/or when it becomes a hassel to replace electrodes.