Astronomy is, essentially, the study of electromagnetic radiation received from the sky. At its most basic, the use of a telescope allows an individual to view the visible part of the electromagnetic spectrum - quite simply gazing at the stars. We've all done it - strictly speaking you don't even need a telescope, though it becomes more interesting with the ability to zoom in. X-ray astronomy, however, is a little more involved and focuses on a separate part of the electromagnetic spectrum, normally invisible to the human eye.
X-rays were first observed in 1895 by Wilhelm Röntgen, a German scientist who stumbled on them quite by accident whilst experimenting with vacuum tubes. A short time later he took an X-ray photograph of his wife's hand, which clearly showed the bones of the hand, along with her wedding ring. The X was initially chosen simply to indicate the unknown nature of the radiation, but became common despite Röntgen's objections.
X-rays simply offer a new way to view objects. Active galaxies, binary star systems, black holes, pulsars and neutron stars all provide far more interesting emissions of X-radiation than everyday visible light. So, in June of 1990, the United States launched a German-built satellite to record these X-rays received from the sky. Referred to as ROSAT, this joint venture was in fact called Röntgen Satellite, for obvious reasons.
Why the need for a dedicated satellite to observe X-rays from space? Simply because although more energetic X-rays can travel through air for a few metres, the earth's atmosphere is more than thick enough to absorb nearly all X-rays from space. So, to view these X-rays from space, the X-ray detectors must be flown above the earth's atmosphere, either by placing the detectors in the nose cone of a rocket (first achieved at the White Sands missile range with a V2 rocket), by elevating a detector with a balloon (a more recent attempt being the High Resolution Gamma-ray and Hard X-ray Spectrometer - HIREGS), or the aforementioned satellite.