Distillation is the process of separating different substances based on different boiling points. In water purification, the water will boil before any of the impurities. Thus the water is evaporated, collected and condensed in a separate container.
The energy source for a distiller can be a variety of things: solar, fire, electricity. Ideally, the energy requirement for a distiller is whatever it takes to boil water. The specific heat of sea water is just under 4 kJ/kg-K but varies a bit with salt concentration. The heat of vaporization, which is the energy require to convert water at 100C to steam at 100C is 2260 kJ/kg. Actual energy requirements will be higher due to losses, however it is possible to recover some energy when the steam is condensed back into water.
There are plenty of small scale distillation systems available. They are designed for distilling tap water but I don't see why seawater could not also be used. Most produce water at about 1 gallon per 3-4 hours. These systems sell for about $100 to $400. Larger systems can produce water faster but sell for $1000 or more. Here are links to several products I've found worth mentioning: http://www.alerg.com/page/A/PROD/MF-WW/WF5300 http://www.webeatprices.com/product_info.php?cPath=1&products_id=1&osCsid=81e2273cd1f96301570520a28565839e http://www.a1-water-distiller.com/
It appears that distillation is not too effective at the removal of chlorine. A carbon filter will probably have to be added to the design.
I think this method has a lot of potential. It is a safe, easy device that could be be constructed using very few materials. The energy requirement is higher than RO but at this scale it might not be too significant. The major drawback with this device is water production. A gallon per few hours is low. However a larger device could speed that up but still nowhere near the level that RO can produce.