Talking about Quake3 based games, and CoD 4/6/8 in particular, in RefDef we have both viewAngles and viewAxis. I'm not really sure what viewAxis is. Quake3 refers to it as simply "transformation matrix", and I've read this topic: a i mbots.net/threads/22099-Converting-3D-World-Coordinates-to-2D-Screen-Coordinates, and it is pretty nice, but unfortunately the author only comments viewAxis like so:

Most games make use of either trio of angles that represent the yaw, pitch, and roll of a player's view-port relative to some origin (usually facing directly North or South, East or West, directly above or directly below) or a trio of 3D vectors that represent the same thing, but in vector format.
I don't really see how you could store the information about your angles which fits into 3 floats in 3 vectors. What kinda vectors are they? What do they describe? I have no problems with math and actually this is what I'm asking for, a mathematical explanation of how and what for this is used. Thanks for your help.