I wouldn't really call them planes (I guess you can jump, though I never did often, especially since its mapped to Select in the PSP version), more like lines, but yeah. It's a way of adding a third dimension of movement without having full out Free Run.
There's a Force Gauge and a Rush Gauge. Your Rush Gauge gradually fills while you're attack and cools down when you sustain a hit while guarding. If your Rush Gauge is empty and you're hit, you'll have a guard break. Your Rush Gauge being higher allows you to deal more damage, but in return you also take more damage and recover less HP (you recover HP gradually from various things, including Annie's circles). The reverse is true for a lower Rush Gauge. You can manually manipulate your Gauge by guarding then pressing up or down, also.
The Force Gauge has four directions and you can assign an arte to each. You can use the arte at any time, but it does more damage if you wait until the Force Gauge is full for that arte (basically, this mechanic allows spamming but punishes it by nerfing artes' power). Also, higher level artes (there's some ougi/tokougi/etc naming scheme that I never can remember) are accessed in a peculiar way. If you use an arte while your Rush Gauge is higher than half, any full Force Gauges will light up yellow and allow you to use a higher level arte.
Yeah, there's a lot of depth. You don't have to worry about TP, and you can spam, but it's not broken at all because your attacks get really weak and it's not worth it.