Short answer: It's not well-defined. Or even poorly defined!
Long answer: Way back when, people noticed there were 5 starlike objects in the night sky that moved: Mercury, Venus, Mars, Jupiter, and Saturn. These were called the Planets. Then Herschel discovered Uranus, and Adams/Leverrier/D'Arrest and some other dude I forget discovered Neptune.
Then, in 1930, Pluto was discovered. It too was immediately called a Planet - though admittedly it was initially thought to be far larger than we know it to be today.
Now - recently, people have started wondering if Pluto is too
small to be a Planet, without having a rigorous definition of
what a planet is. This strikes me as sloppy thinking.
I think we should have a rigorous definition for Planet, and since they were originally defined by example, I think today's definition should accommodate the past. The best one I've heard is here (from Gibor Basri)
A 'fusor' is a star - an object big enough to generate its primary heat through fusion.
This gives us an upper and a lower boundary on the size of a planet. If the body is too big, it begins to undergo fusion in its core, and it is some type of star. If it is too small, its gravity is not strong enough to pull the shape into a roughly spherical one.
This sounds like a workable definition. There's a couple corner-cases
to resolve - like how spherical does an object have to be to meet
this criteria? I'd say the difference between the lowest and highest
points on the object should be under X% of the rotation-adjusted
radius - and X should be 10 or so.
The interesting thing is, this adds significantly to our collection of planets. Major asteroids like Ceres are now planets, as are Chiron, Quaoar, and Sedna. Though they wouldn't be (probably) if we dropped X down to 5.
I think we should subdivide our collection of Moons too - into Major Moons and Minor Moons. Major Moons would be planets if they orbited the Sun by themselves. Minor Moons are too small to fit the Major Moon criteria.
(update 3/15/04) The airwaves are buzzing about Sedna. It is clear that Pluto and Sedna should be classified the same way - and most of the Astrogeeks I know seem to favor classifying them both as non-planets. I still favor calling them both planets.