The cornerstone of Einstein's General Theory of Relativity is his observation that gravity and acceleration are indistinguishable. Put someone in a rocket that accelerates through space at 9.8m/s (35km/h) and their feet will be glued to the floor of their cabin just as if they were experiencing gravity on the surface of the Earth. Of course, accelerating at 9.8m/s in a straight line forever isn't a very practical way of simulating gravity. A better way is to exploit "centrifugal acceleration", an effect in which someone spinning, for instance, on a merry-go-round, appears to be flung outwards.
This is the phenomenon that Arthur C Clarke exploited in his film 2001: A Space Odyssey. In the film, Dr Heywood Floyd's shuttle docks at the axis of Space Station 1, a 275m (900ft) diameter, slowly rotating wheel. As he makes his way outward along one of the spoke- like corridors, his weight (which is a measure of the gravitational force acting on his body) gradually increases until finally, at the rim of the station, it is close to his weight on Earth.
Of course, it's not quite the same as gravity on Earth. If Floyd drops an object, it does not fall directly to the floor, but appears to be deflected in the opposite direction to the space station's rotation. This is known as the "Coriolis effect". The Coriolis effect illustrates a subtle point that was recognised by Einstein: gravity is only truly indistinguishable from acceleration in very small volumes of space. This means that, although it is possible for us to simulate something like the Earth's gravity, we can never really do it perfectly.