Put simply, blur refers to the part of an image that is out of focus.
There are two types of blur, broadly speaking, focus blur, and movement blur. Focus blur is where the image, or part of the image, is not in focus, and Movement blur is where the subject or the camera has been moved while the shutter was open.
While it is assumed that blur is bad, often that is not the case at all. For example, by using a shallow depth of field
in a portrait, you can intentionally blur the background, which draws attention to the subject.
Likewise, you can choose to let a moving object blur slightly, to accentuate its movement.