Blurring your image can be a good thing or a bad thing. Unintentionally missing focus can completely ruin your image, this is definitely something you want to get right in camera...there's no fixing it with editing. On the same note, intentional blur can add drama, intrigue, or beautifully separate your subject from the background. Intentionally blurring your image can incite emotion or tell a gorgeous "emotive" story.
Take in the scene before you. Notice how space separates the objects in front of you, not to the side. So the more near an object is to the focus area, it will be sharper and focused while farther away objects will blur more and more the farther back they are. This is called "depth of field." Anything to the side will be in the same "plane" as your subject so it will also remain focused.
Typically you'll want to focus your image on the closest subject to you. But not always...mixing it up a bit can create a whole new look and create a different story or a new emotion. I personally like to mix it up because in playing around, you'll also create a sense of space and distance.
So how do you create the blur in the first place? You'll need to look up how to change your "f-stop" on your camera. Depending on which lens you have, you'll be capable of choosing between an f1.4 all the way up to f32, I believe. The smaller the number, the more blur you get. The higher the number, the more you'll get in focus. I typically shoot between f1.8 and f2.8...basically the smallest number my chosen lens will allow. Shooting at such a low number will make it harder to focus where you want, so it takes practice but it's well worth the effort.
A bonus effect of intentionally using blur is creating bokeh because a light source is out of focus. It can be great for adding a little something extra pleasing to the eye.
Intentionally blurring the entire image can help it to appear more emotive or help you to tell whatever story you want. Maybe you want to just be artistic? or maybe you want to show that something feels not quite right or difficult to you?
When is intentionally blurring your image not a good thing? That varies from person to person but for me, I'd say landscape images. You want to see the whole landscape nice a crisp all the way through, blurring it too much would make it difficult to see the glory of the nature scene in front of you. Unless you want to single something out. This also applies for a trip or weekend getaway, you want to see the things that you normally don't see. I'll also blur less if I'm creating a silhouette or shooting the night sky.