In 1800 Herschel discovered Infrared (he called them Caloric Rays because they felt warm). Like any good scientist, he wondered if something similar could be found on the violet end of the spectrum. Alas, when he set up his thermometer on beyond violet, he didn't detect any heat. Oh well, he said, and focused on what he knew.
Then in 1801 Johann Wilhelm Ritter refused to be daunted by the violet end of the spectrum. See, he'd read Herschel's paper, and thought that Herschel hadn't gone far enough in his investigations. As a chemist he was familiar with the photosensitivity of certain chemicals. He knew that silver chloride turned dark when exposed to sunlight, reacting stronger to blue light, rather than red.
When he exposed a piece of paper coated with silver chloride to a spectrum, he discovered the strongest reaction was in the “invisible” side of violet light. Because of the chemical reaction, he named this invisible band of light “deoxidizing rays” or “chemical rays”. Essentially, he was one of the first to create a "photo-graph", or a literal recording of light.
He'd discovered Ultraviolet.
But what he also discovered was ionising radiation.
The electromagnetic band is divided into two different kinds of radiation: non-ionising waves, like radio waves, and ionising radiation, like X-rays.
Ionising radiation is radiation that's strong enough to knock electrons off an atom or molecule. The ability to cause a reaction in a chemical such as silver chloride is due to ionisation. It's the scary stuff that can potentially damage DNA and cause cancer.
Fortunately, most of the harmful ionising radiation (from UV on up to gamma rays) gets filtered out by our atmosphere. Still, visible light and some near UV get through. These are the frequencies that start to chemically affect stuff. (This is also why you don't store your beer in sunlight.)
Non-ionising radiation like radio waves can pass through our atmosphere, but doesn't pose a threat to us. (FYI, the radio wavelengths that mobile phones use is safely in the radio waves range. Mobile Phones do not cause cancer. Feel free to carry them in your bra.)
Ah, so what's the benefit of the ultraviolet spectrum in astronomy? It's good for detecting hotter objects. UV is very good for detecting chemical composition, very old stars or very young stars, and for identifying star-forming regions, which denotes active galaxies.
This UV images of the Andromeda Galaxy (M31) shows it's active star-forming areas:
When the variable star Mira was imaged in UV by GALEX in 2006, scientists were amazed to discover it had a tail. Mira moves through space rather quickly for a star (130km/s), so fast, it even has a bit of bow shock in the interstellar medium (ISM) and a tail of matter streaming behind it for thirteen lightyears:
Her Grace likes to think of UV as the "hot and bothered" frequency.