Building up the orange gauge on the bottom of the screen is important if you want to unlock new combos and other in-game unlockables that are otherwise inaccessible. However, it may not be clear on just how to do so.

Using Nariko, try to score consecutive hits on enemies to build the number on the left side of the gauge up as much as possible. If Nariko is injured or waits too long in between scoring successful hits, the number will reset (though the progress made on the gauge will remain). With Kai, you must score consecutive hits as well, though building up the gauge is made considerably easier because her time constraints between hits are much more lax, and her use of aftertouch (when shooting arrows) allows you to guide the arrow to its intended target.