Why does a dentist lay a large lead apron across his/her patients torso when his/her teeth are being x-rayed?

X-rays are not as focused as people think. This website will tell you how they work, HowStuffWorks "How X-rays Work". The X-Ray radiation is scattered about the room, that is why technicians typically leave the room to do any X-Ray. The apron covers your vital organs, preventing them from getting any unnecessary radiation.

Hello robo

Indeed as bigbopper posted X-rays do not form a narrow beam, but stray into all directions.
The apron is to shield the rest of the patient. The straying X-rays are also the reason why all staff leaves the room and protect themselves behind a X-rays shield in the wall between.

Note : the yearly dosis of X-rays should be kept as low as possible. Besides medical X-rays there is also a daily dosis of background radiation.