Well first of all, if you are using your phone camera, that's a pretty good reason... although there are some that can take great pictures. But, the biggest culprits are 1.) "camera shake", 2.) lens, and especially the length of the lens and 3.) low light. These three things pretty much go hand and hand. It seems pretty obvious that you should keep the camera still when taking pictures, but when you are chasing children, trying to get a smile, etc... it can be challenging. Many times I have the perfect shot, but because I was doing something goofy to get a smile, the camera was too unsteady and the picture blurred. The second picture I attached is an example of this. The longer the lens, the more challenging this becomes, because it is even harder to keep all that equipment steady. Then add the factor of low light into the picture (a dimly lit church for your child's Christmas program, a poorly lit living room, etc...) and keeping the camera still becomes even more vital, because you are having to use a slower shutter speed to let in more light.
Another factor is focus, and if you are using a prime lens such as a 50mm lens, you are in one way at a huge advantage because this is an awesome lens for portraits, is usually very sharp, is relatively short, and works well with low light. However, if you do not learn how to focus correctly, you will have a finger or hair bow sharp and in focus, while the eyes are blurry and out of focus. When most people look at a picture, the eyes are the first thing they see. I have become extremely particular about this.
All of this being said.... here are my tips for avoiding blur:
1.) Make a conscious effort to hold your camera steady.
2.) Consider investing in a good lowlight lens that is not too heavy or long, such as a 35mm or 50mm (and learn and practice focusing properly, always trying to focus on the subject's eyes).
3.) In low light situations use a flash so that you can use faster shutter speeds (using slower shutter speeds and higher ISO setting let in more light if you are not able to use a flash, or do not own a speedlight flash). I have talked about some of these points in previous "tip" posts.
In the first picture, although I did some extra skin smoothing and eye sharpening, I had a good, sharp picture to work with. The body and background are somewhat blurry, and the face is very crisp, which is exactly what I wanted. I did not even present the 2nd picture because although the baby is smiling, unfortunately the face, and especially eyes, are too blurry, and this is not the type of quality image I want to offer my clients. Look at the buttons on the dress, slightly blurry in the first picture, and sharp in the 2nd. My focus was off, and I also probably moved too much when I took the picture. I always have plenty of good shots to make up for a few bad, and although editing can do wonders, it typically can't make a low quality, blurry picture great, no matter how much you sharpen in editing software.