How smooth the transition is between a photo's highlights and shadows determines if you have hard or soft lighting. If shadows are very sharp, it is hard lighting. If the shadows are more of a gradient and blurry, then it is soft lighting.
Any light can be hard or soft. Softer shadows are caused by a light's ability to bend around the object being photographed which depends on three things:
Hard lighting has more contrast and is used for a more dramatic or edgy effect. It can also point out skin imperfections more easily like wrinkles. Soft light is more flattering so more often used for portraits.