The Byakugan is a Doujutsu bloodline ability specific to the Hyuuga clan. It gives the user a 360 degree field of vision except for one small spot where the spine and skull connect.It also allows the user to see chakra points in the body which is the secret to Juuken, or Gentle Fist, the type of Taijutsu the Hyuuga clan has mastered.And I might be mistaken on this, but I believe the Byakugan, like the Sharingan, can see peoples actual chakra and its colors as well.
The Juuken is a special type of Taijutsu. While in traditional Taijutsu you preform strong, direct hits to try and break bones or draw blood, the Gentle Fist style the Hyuuga use attacks the chakra points of the body which only they can see using the Byakugan. They do this by using pinpoint strikes with the tips of their fingers releasing small amounts of their own chakra into the opponent at the chakra points.
This shuts down the opponents chakra flow, and if all the chakra points are hit, causes the oppenent to not be able to use any jutsu.
As shown with the battle between Neji and Hinata at the Chunnin exams, the Juuken can also be used to attack the body's organs such as the heart, which can be fatal.
Lastly, and probably the most understated and untapped part of the Juuken, is that it can also boost people's chakra if struck correctly. (I forget what episode it is exactly but when its explaining the Gentle Fist style it says it can either shut down enemy chakra points or boost them. I'm trying to find the episode now.)
I plan to expand upon that aspect and create a move where the user preforms the Juuken on himself to temporarily boost his chakra flow and power.