I was curious about that recently, and _somewhere_ I found a really
nice explanation. Wish I could point you to it; I won't do it justice.
But the basic idea is that magnetic dipoles (from the electrons in
material) align with the DC magnetic field. If something perturbs
them, they will oscillate with a natural frequency depending on their
mass and the strength of the restoring force: the externally applied
field. Think of a (tiny) bar magnet on a pivot, like a compass needle.
If there is no damping, it will oscillate. The strength of the
externally applied field determines the restoring force, and therefore
the oscillation frequency. The reason given for making the YIG
resonator a ball is to get a very uniform magnetic field through the
whole ball so that all the atomic dipoles have as nearly as possible
the same resonant frequency. The high Q resonance, of course, is what
lets it be a filter or the tuning element of an oscillator. It's very
handy that it's relatively easy to tune over an octave or more range.
However, since the tuning involves changing a fairly large magnetic
field, it's much slower than tuning with a varicap diode.

OK, now that I've written all that, of course it becomes easy to find
the reference: http://pw1.netcom.com/~dstraigh/yig.html Oh, well.

Cheers,
Tom