The Hyuga clan was one of the main clans forming Konohagakure. Most of them are characterized by grey/light-colored eyes. They're known for their kekkei genkai, the byakugan, which is a form of dojutsu.
The byakugan grants its wielder an augmented field of vision. I think it's almost 360 degree vision except for a small spot on the back of their head. Similarly to the sharingan, the byakugan is also capable of perceiving chakra, but can also find chakra points. Because they can perceive those chakra points, they've also built a fighting style revolving around those: gentle fist. This fighting style mainly focuses on close-ranged combat where the user hits a target's chakra point with chakra-enhanced fingers of palm, blocking the target's chakra paths among other things and basically inflicting internal physical damage.
Good, you touched on a few good points in regards to the abilities of the clan and the lore. Now lets dive deeper in terms of details what are all the passive and or innate capabilities of the Byakugan. You mentioned 360 degree vision what else is there?
The byakugan also grants its user the ability to see through objects, like walls. We also become able to follow and read quicker body movements so an increase in our tracking speed (equivalent to 3T sharingan's tracking speed?). A byakugan user can also recognise where chakra signatures originate from, so you can tell if a "character" is a clone or not. And we can also see people's chakra pathways and tenktetsu.