Some folks like their photos sharp and literal, but sometimes it is fun to intentionally leave things a little blurred. Done well, this can give the image a little more energy and movement, as well as make it a bit more abstract. The key for living subjects is to get a combination of a relatively sharp head and eyes along with the motion blurred remainder of the image.

Here is shot from Costa Rica that has a bit of that balance.

Grey-crowned Central American squirrel monkey in tree, Manuel Antonio National Park, Costa Rica.

Grey-crowned Central American squirrel monkeyCanon 1DX.  500mm.  ISO 800.  f/11 @ 1/80 second.