These are very short wavelength (high frequency) electromagnetic waves.
Because they have such a short wavelength and high energy they pass through most substances. This is why they can be used to take pictures of the human body. X-rays pass easily through most of the soft parts of our bodies, but get stopped by the bones for example. A medical X-ray taken to study damaged bones is therefore really just a picture of the shadow cast by the bone.
X-rays are also extremely useful for studying astronomical objects. This is because X-rays are only emitted by objects when they get very hot. If we want to study objects, or parts of them, that are very hot (a million degrees or more) we must study the X-rays they give off.
On the other hand if, to start off with, we don't know which objects are hot, we can scan the sky with X-ray cameras and see which ones give themselves away by emitting X-rays.
One major problem for astronomy though is that the Earth's atmosphere absorbs incoming X-rays - so the X-ray observations have to take place in space.
One major advantage for life on Earth is that the Earth's atmosphere absorbs incoming X-rays and so protects us from them!
X-rays were first discovered by German scientist called William Konrad Röntgen (1845-1923). Röntgen knew he'd made an important discovery but he didn't know what to call this new radiation so he just called it 'X-rays', planning to think of a proper name later. He never got round to it! In some places (particularly Germany) X-rays are called Röntgen waves in honour of the man who discovered them, but generally the word X-ray has stuck.
See some images of the Sun in X-Rays in our solar explosions section