Sharp images are generally the desirable outcome of focusing. Not necessarily all of the image but the elements that we want to be sharp. Sometimes a blurred, or unsharp image is acceptable, when capturing rapid motion for example, but even here a point of sharp focus is desirable, upon which the eye can come to rest. An absence of this can lead to a feeling of dissatisfaction in the viewer.
There are other factors that affect image sharpness not related to focus. Camera shake for example, often as a result of using a shutter speed too slow for the focal length of the lens. The longer the focal length of the lens then generally the faster the required shutter speed for hand held unsupported camera work.
Image Stabilisation (IS) or Vibration Reduction (VR) can help with camera shake and 'gain' you an extra stop or two. The optical types (rather than digital) are usually the better. Be aware that they should usually be switched off when the camera is used on a tripod or other well braced situations.
A shutter speed too slow for the motion of the subject will also lead to blur. This was also discussed in the Exposure section. Learn to pan smoothly with the subject or wait for natural pauses. A blurred waving hand can add a dramatic effect, a blurred moving head, can look a mess.
Modern cameras and lenses tend to have auto-focus functionality. This usually requires a reasonable amount of light in order to work effectively. Too little light, or contrast, in the subject matter and an auto-focus system will often fail to focus-lock. In extreme cases it will rack fruitlessly up and down its focus range as it tries to acquire focus. This can waste precious time and lead to lost shots. The more light that can reach the focus sensors the better. This implies that faster lenses (those with a large maximum aperture, f2.8 or wider) will be more efficient at focusing in low light.
Often the best strategy is to switch to manual focusing. Use the auto focus indicators as a guide to when the image is sharp but also use your own judgement. After all, before auto-focus that was the way that cameras worked! Try focusing on an edge, lips, an eyebrow, something which offers a course texture, rather than skin tones. Most cameras offer a focus-lock facility whereby you can re-align the camera to place the focusing sensor over a region of the subject that offers easier focusing then press the focus-lock button. Often half pressing the shutter release can do the same thing but might also lock the exposure, so be careful. Get to know your camera and its configuration options.
Moving the camera, focusing, then re-composing can often be faster than trying to move the focus region around in the viewfinder, as many modern cameras allow. That has its uses, but don't waste time chasing the focus target around the viewfinder.
Sometimes it is possible to pre-focus on a spot and then wait for the actor to move through that spot.
Another general rule is that if an actor's face features prominently in the frame then the eyes should be the sharpest element in focus.