"Style" can be treated as a special Background. The number of dots you have in your "Style" determines the maximum amount of Power Points you can spend on a maneuver available to that style. New characters receive 5 dots for their Style. Most put all 5 in one style. But you can split it 3/2 or 4/1 or 2/2/1 or 1/1/1/1/1 (restricting oneself to a lot of weak 1 PP maneuvers) to know multiple Styles. One can not spend Freebie Points on increasing your Style background. Characters should choose a "Primary" style. This determines their Chi/Willpower values and represents the first style they studied.
Increasing the "Style" background costs 5 x the next level in Experience Points. Remember, your "Style" background limits the Power Point cost of the maneuvers you can purchase. That's why most smart fighters take that first 5 free points and put it into one style. It's more difficult to raise Styles later on.
The advantages of having multiple Styles, of course, is the flexibility of choosing maneuvers. When a maneuver lists different Power Points costs for multiple styles, the fighter is able to select the least expensive cost for the style available to them, limited by their Power Point cap, of course. "Any" maneuvers are included in the PP Cap, so if a fighter learns Multiple Styles, many "Any" maneuvers that cost 5 PP are no longer available (until I raise a style to 5 dots with XP).
So, if I had Special Forces at 4 and Wu Shu at 1, and I wanted to get "Pin", it costs 4 PP for SF and only 3 PP for Wu Shu. Unfortunately, 3 is over my PP cap for Wu Shu, so I have to purchase it using Special Forces at 4 PP.