In 3D fighting games, the axes determine the depth of your range with the opponent. “Tracking” is an important part of dealing with those axes; while 2D games have the matter handled quite simply (i.e., characters only have to turn around automatically when they need to), without the player utilizing tracking tactics in a 3D game, characters go wheeling off in bizarre directions, and it becomes difficult to trick the opponent into getting hit at all.
Because 3D games have a literal depth factor (physically thinking), this is perhaps a defining component that differentiates them from 2D games. This component exists in nearly all fighting games called 3D (as opposed to 2D fighting games with 3D graphics). Tracking is highly important to consider during general conduct, juggling, and so forth (though it is harder to explain than it is to envision... because humans live in a 3D world, tracking is actually second nature in practice).
In recent 3D fighting games (think Tekken 3 and later), shifting the axis at will is almost always an option: of note, the Tekken series prefers “sidesteps” (note that in T2, having a sidestep was a godsend; T3 gave them to everyone, which certainly helped the 3D feel by far), as does Virtua Fighter (VF3 had an “escape” button; simultaneous presses take care of this function in later titles), and the Soul series has “8-Way Run” (so that jumping, which is risky anyway, is harder to perform).
By shifting axes like this with your opponent, you can avoid his vertical attacks. However, horizontal attacks carry the possibility of tracking you to the direction you sway (so you must use good judgment as to whether, and which way you should sidestep). This is one of the most characteristic tactics of 3D fighting games (and is probably taken to its biggest extreme in the Soul series, where it boils down to a rock-paper-scissors system).
This also lets you wrap around behind an opponent sometimes, which is as close to crossup as you get in 3D games.