Blur is a graphical effect that aims to imitate an unfocused image. In a photography context blur can occur when the focal point of the lens is not at the right position of the target of the photograph. Also blur can have other origins. Blurs can happen as the result of a poor exposure during its recording (too long exposure time for a large movement of the object or a high movement of the recorder). Also blurring occurs when you use a very wide aperture (f4). In that case the objects that are out of focus are very blurred compared to the situation where the aperture is fully closed (f22).
In a graphical context, blurs are effects that imitate those situations (with more or less success).