Portrait photography often means short depth-of-field. In fact, when the photographer is close to the subject and a low aperture (such as f/1.8) is used, then the depth-of-field an be as short as one inch (3 centimeters?). Even slight variations in focus can take the focus off the model's eye and make it slightly blurry. In portrait photography, the eyes must be in perfect focus, but we don't mind leaving the skins slightly out of focus because it adds to the smoothness of skin.
Many beginning photographers are taught to use the center autofocus point, obtain focus while pointing that center focus point on the eye, and then recomposing so the eye is placed according to the rule of thirds. This technique is called focus and recompose. When this technique is used, it changes the plane of focus just slightly. Often times, when extremely short depth-of-field is used, this can throw off the focus on the eye. Even just moving the camera to recompose may mean the photographer scooting back or forward a half an inch, which will remove sharpness.
When extremely short depth of field is used, it is preferable for photographers to change which autofocus point is used rather than always using the center autofocus point and then recomposing the shot. This may annoy you for a few weeks after switching to this method, but in the long term, your sharpness will thank you. Almost all professional photographers use the focus point selector rather than the focus and recompose method when shooting short depth-of-field.
There's a catch to all of this. If you're shooting an entry-level DSLR, you probably don't have many autofocus points on your camera. Many entry-level DSLRs only have 9 autofocus points. Sometimes this might work out and an autofocus point just happens to be available where the model's eye is; however, you will find many situations where there simply isn't an autofocus point to cover the place where you want to focus. For this reason, the focus and recompose method is more practical for entry-level DSLRs. If you have lots of autofocus points, however, then consider forcing yourself to switch over to the compose and focus method.
Once you're comfortable with the basics of how focusing works and you're feeling a bit more adventurous, you will want to learn how to do back button focusing.