Try rotating the object, with the pivot point at 0,0,0 and the vertices centered around 3,3,3. You will see the difference.
EDIT: here's code to demonstrate...
// set window properties
SetWindowTitle( "Test set pivot" )
SetWindowSize( 1024, 768, 0 )
// set display properties
SetVirtualResolution( 1024, 768 )
SetOrientationAllowed( 1, 1, 1, 1 )
// these are to show where world 0,0,0 is
ObjectVertical = CreateObjectBox(.1,100,.1)
SetObjectColor(ObjectVertical,255,0,0,255)
ObjectHorizontal = CreateObjectBox(100,.1,.1)
SetObjectColor(ObjectHorizontal,255,0,0,255)
// this object keeps its pivot point at
// its local 0,0,0 (center of the object)
// much like your head pivots around its center
ObjectOne = CreateObjectBox(3,3,3)
SetObjectPosition(ObjectOne,0,3,0)
// this object will have its local center at
// the worlds 0,0,0 point (the sphere)
// much like your arm pivots on your shoulder
ObjectTwo = CreateObjectBox(6,1,1)
SetObjectPosition(ObjectTwo,-3,0,0)
FixObjectPivot(ObjectTwo)
do
// rotate each object around its local center
RotateOBjectLocalY(ObjectOne,.5)
RotateObjectLocalY(ObjectTwo,.5)
Sync()
loop
By adjusting the object's world position before you fix its pivot point, you can make the object's "center" be virtually anywhere.
For instance, your arm doesn't pivot at its center, it pivots at your shoulder. And your forearm pivots at your elbow, etc.
MORE EDIT: I'm going to submit this to the help file. I've changed the example up a bit, so if you're not seeing the image below, copy it again