Hard and soft are terms used to describe the characteristics of light.
Hard light is produced from a small single source and creates hard shadows. Hard light is used to add drama to a scene as it provides quick fall off to create sharp shadows.
Soft light, by contrast, is produced from a much larger source of light and creates soft shadows. To create soft light, you need to use light modifiers such as softboxes or diffusion to shine your light through. Soft light is more flattering on the face than hard light, so soft light is often used for interviews and filming people.
Everyone has experienced hard light and soft light. On a cloudless sunny day, the sun is the primary source of light. It is a small object in the sky and therefore creates hard shadows. However on a cloudy day, the sun is shining through the clouds. The clouds diffuse the light and become one massive light source, resulting in very soft shadows.