Purposely blurring an image can serve a range of purposes and convey a variety of different meanings.  

Blurring can occur through motion of the camera, motion of the subject or shallow depth of focus in the camera settings.  The juxtaposition between a blurry portion of an image and a portion of an image that is razor sharp can be particularly effective, often conveying a strong sense of Emphasis.

Blurring can also be achieved post-production through image processing (Photoshop).

Here are some effective examples of purposely blurred photography. Below the images are links to more information. Explore them or do your own web research to gather ideas for your Blurred project.

http://www.digitalcameraworld.com/2012/03/02/in-pictures-30-great-examples-of-motion-blur-photography/

http://digital-photography-school.com/a-beginners-to-capturing-motion-in-your-photography/

http://www.smashingmagazine.com/2008/08/24/45-beautiful-motion-blur-photos/

http://digital-photography-school.com/13-places-to-practice-taking-beautiful-motion-blur-images/