Damnit, I wrote a much longer reply but it must have been eaten by the power goblins (
http://www.penny-arcade.com/view.php3?date=2002-11-25&res=l ).
Basically, matricies can be thought of as 4 vectors, typically aranged vertically, which are the x, y and z axies and a translation. Thus you perform a rotation/scale/shear by messing with the vectors, and can represent any arbitary transformation in a single matrix. By multiplying two matricies together you form a new matrix with is the result of both transforms. By multiplying a point by a matrix, it is transformed by the operations represented in the matrix. You transform a vector in the same way, except that you don't perform any translation.
Spaces then.. World space is your entire virtual universe, with some arbitrary reference point. This origin may be a corner of your level, middle of your heightmap, center of the earth etc. It contains everything that is 'physical' in your game (and a few things that aren't
) Object space is a things personal coordinate system - say when you create your 3d model, this is where the origin is, the center of a ball, the feet of a person, etc. Camera space is that with the origin centered on the camera, usually with the x axis going left/right, the y up and the z into the screen.
Moving from one space to another is (easily?) represented by a matrix transformation. So, object->world will be how your model should be positioned in the world in regard to everything else. World->camera defines how a world is viewed, the world is moved into the camera space at the correct position, and hence the camera appears to move around the world. Then usually you multiply by a projection matrix to collapse the whole scene (still fully 3d and orientated around the camera) into a single flat plane - possibly appying perspective whilst doing so. Now wash, rinse and repeat for every single vertex, and you're halfway to having a complete frame drawn..
Moving
backwards along this chain is done by multiplying by the inverse matrix at each point (note that you can't usually undo the projection matrix though, you'll get a line in space, not a point). Finding the inverse of a matrix is something i've managed to avoid so far, the maths gets a tad sticky. There may be a function in j3d for this, I can't remember though.
That may or may not have made no sense at all
Hopefully it gives you some ideas though..
