There are some photos in which the blur is not a defect, irreparable damage, but is in fact an added value that was made intentionally!
In these cases, we speak of a creative blur. It allows you to obtain extremely varied results, from the pictorial touch that intentional blur can impart on a landscape, to the prominence it gives to moving subjects in which static subjects are also present in the frame.
It's all a blur by Susan Blick Photography
It's all a blur on the streets of New Delhi. Well, that's how it feel sometimes. This is a long exposure taken in the heart of the Parharganj.
Creative blur can be achieved in two ways. The first is to use long exposure times, stand still (best done with a tripod and remote shutter release) and photograph a moving subject.
The second is to use long exposure times and move the camera while photographing a static subject.
Umbilical by Tanya Rowe
Are we connected to our phones like our life depends on umbilical chords at the very beginning?
This is known as ICM: Intentional Camera Movement and is a genre that can undoubtedly expand your photography since it allows you to offer a different and somewhat romantic vision of otherwise trivial subjects.
Yellow Blur by MarinadeWit
Natural light, indoor shot of yellow flower. I added the blur in PS and really felt it worked with this image. Nikon D7200, Nikon 105mm macro Auckland Wintergarden
Since capturing movement is a photographic delight that is expressed in many different ways, there are also other techniques that can assist you with creating the blur effect. For example, panning, zooming, or even camera tossing (the latter a little extreme, because it consists in launching the camera into the air which we don't advise trying unless it's an old camera that you don't care about!).