Relativity, as we know, explains the intimate connections of space and time, since they are essentially components of one larger entity, the spacetime continuum.
One of the more elusive byproducts of this theory is the concept of gravitational waves. To explain, first understand that the spacetime continuum has curvature, and this curvature is directly affected by the mass of an object. For instance, large masses like planets will actually cause spacetime to "bend" around it.
And gravitational waves are like any other waves, in that they are ripples that travel outwards from the source - these in particular, though, are ripples in spacetime, which travel away from the source carrying energy in the form of gravitational radiation. Again, this is just a theory by Einstein, but I'd keep an open mind about it. Because, you know, he's Einstein.
So what objects produce these waves? Well, they have to be accelerating. But more than that, this motion cannot be spherically or cylindrically symmetrical. Gravitational waves HATE symmetry.
Just by looking at these numbers (G^4)/(c^5) these are extremely small numbers we're dealing with. For instance, the Sun-Earth system gives off a whopping 200 watts - absolutely paling in comparison to the electromagnetic radiation emitted by the Sun (3.86 * 10^26 watts).
Tune into my next post (which will be in about 10 minutes) and I'll discuss gravitational radiation's implications on orbits n' stuff.