Taking photographs of our children is probably the form of portrait photography that is most familiar to most of us. The most common mistake we make when we're focused on capturing a good expression is to forget camera blur. And today's high resolution digital cameras make even slight amounts of blur more obvious.
The first step in preventing blur is to master the basic technique of keeping your elbows propped against your torso and pressing the shutter-release button smoothly. You can also enable the lens vibration reduction feature to effectively reduce blur and let you concentrate on getting a good shot.
Another form of blur is "subject blur". You've probably taken photos of your kids playing in the park or doing sports where the background is sharp but the most important element, your main subject, is blurred. This blur, caused by the subject moving while the shutter is open, is known as "subject blur".
Subject blur can be prevented by choosing shutter-priority auto mode. Pick a shutter speed and let the camera adjust aperture for optimal exposure. Choose a shutter fast enough "freeze" your subject's motion and prevent subject blur.