Basically the title,

Chakra jump can cancel unwanted programed motions in the game.

An example of this is if you simply jump straight up and down your CAC (create a character) will touch his/her hand to the ground when he/she lands, then stand up.

If you were to press chakra jump the moment the CAC lands and then immediately press regular jump the motion is canceled and you can jump again right away.

You can also do 3 basic "jumps" together 2 different ways before you have to land, usually i like jump-dash-jump but it can be jump-jump-dash.

Once you get use to these 2 concepts you can add them together jump, dash, jump, then chakra jump when you land, and immediately jump, dash jump repeat.

You'll also notice a little more speed compared to not using chakra jump, and little more momentum.

It can be used to quickly move off walls as well.

You can see in some of my runs the chakra jump indicator when I land before I hit jump. My CAC's hand won't touch the ground but it is not always needed so may not always do it.

In general it's not hard to pick up and can save a lot of time.