These fabrics are the 'offspring' of traditional hard shell outer layers and the soft fleecy mid layers. Frequently, softshells have an outer fabric that is a little softer and stretchier than a true hard shell that is laminated to a soft inner fabric. In some cases, there may be a microporous membrane between the two layers, but it's not a requirement.
Soft shells are generally considered to be highly water repellent, but aren't quite at the standard of water proof. They can vary in 'warmth' depending on what style of inner fabric is used. Inner fabrics can range from a smooth brushed jersey through to a high loft fleece. Softshells are ideal jacket or pant fabrics for shoulder seasons or for winter in temperate climates.