A X-ray is an Electromagnetic Wave of high energy and very short wavelength. X-rays are able to pass through many materials. When X-rays come into contact with you they pass through the soft tissue in your body because the soft tissue cannot absorb the X-rays. The X-rays continue through your body until they reach something denser such as a bone or piece of metal. The X-ray then bounces off the denser material and can be captured by film.
Do you have to be worried about your privacy at airport security? The answer is no. When the scanners were first introduced, many travelers had concerns about personal privacy and the images seen by TSA agents. Rest assured, the scanners show only a generic outline and only highlight areas of concern or where something is out of place.
However, carry on luggage is scanned by CT scanners and those can see everything. Don't worry, those are only for your safety so security knows nothing illegal is carried on a plane. CT scans transmit X-rays onto the luggage which then travels digitally to a computer.
In conclusion, these scanners are for your personal safety and you do not need to be concerned.