General relativity describes gravity in terms of the curvature of space time. A gravitational wave is a fluctuation (a ripple) in the curvature that propagates as a wave, travelling at the speed of light, and transferring energy.
General relativity predicts that gravitational waves will be generated by massive accelerating objects, for example a binary star system (two stars orbiting about their common centre-of-mass). You can think of gravitational waves as being analogous to electromagnetic waves, which are generated by accelerating charges.
Gravitational waves have only been detected indirectly so far: detailed observations of the Hulse-Taylor binary pulsar (a binary star system containing a pulsar, i.e. a rapidly rotating neutron star) show that the system is losing energy as time passes, which is attributed to the emission of gravitational waves. A number of ambitious experiments using laser interferometry are underway to detect gravitational waves. The images below give a glimpse of what is involved.
The effect of a plus-polarized gravitational wave on a ring of particles.
The effect of a cross-polarized gravitational wave on a ring of particles.
A schematic diagram of a laser interferometer.