Softshell is a recently conjured up name that covers a wide range of clothing, the common denominator being that whilst not totally waterproof, it offers some water resistance in conjunction with great breathability, and a lot of windproofing. These factors are related so that greater weather proofness is available but at the expense of breathability and vice versa.
In many ways, Buffalo was the original softshell, and really, there is little that a soft shell does that Windproofs can't do more cheaply, more lightly, and possibly just as comfortably. However one thing softshell does a lot better than a windproof - it is much more stylish - and of course that is an essential element for success in modern mountaineering (at least it is if you want to get your picture in the mags!). Actually, tongue in cheek aside, softshell fabrics are also more stretchy than plain windproofs, allowing greater flexibility and reach when climbing, and they are much harder wearing.