Every industry has a 'homeland.' For American cars, it's Detroit. For wine, It's France. The outdoor industry put down its earliest roots in the Bay Area, around San Francisco, California. The staggeringly nice weather and wide range of outdoor activities around San Francisco contrasts the city itself, which is predictably cold, grey, and foggy. What does this have to do with North Face, Mountain Hardwear, Sierra Designs, Marmot, and the rest? When their designers traveled from the sunny East Bay into the city, they thought 'we know how to make the perfect jacket for this nasty weather!' And so the softshell was born.
To define our terms, a 'shell' is an outer layer intended to be worn over insulation. The term 'hardshell' commonly refers to waterproof-breathable construction, 'windshell' to a lighter, more breathable jacket, and 'softshell' is a third category.
Softshell is actually a property and style of fabric, and the term is also used more generically for the jackets made from it. The 'shell' is the outer side of the fabric, which is water and abrasion resistant, stretchy, and allows some breathability, or moisture movement through. A knit or fleece lining can be bonded to the inside to improve low-temperature performance. Softshell fabric is not waterproof and so seams will not be sealed, though in high-aerobic activities, the movement of heat through the fabric will displace liquid water as it attempts to soak in. When you're not sure exactly what the conditions will be, but expect cool temps and maybe light precipitation, a softshell can be the perfect jacket. It stretches to allow for range of motion, will keep you dry for short exposures, and can help retain body heat.
Because it is such a good general-purpose jacket, the design and fit of most softshells will closely resemble the classic 'jean jacket,' with a tapered fit in the torso and a fold-down collar. To fit in with its more technical cousins, it will still have adjustable cuffs and a full-length zipper that brings the collar up to your chin. As a result of the fit and lining texture, softshells don't always 'play well' with other fleeces, so be sure to try the jacket on with the insulation you're most likeley to use.
Different brands will use variations in the softshell fabric to achieve more or less stretch, durability, weight, and utility, and may include pit zips, venting pockets, even hoods, but they will be an 'all-purpose' design at heart, so don't be afraid to choose based on your personal comfort.