These explanations hardly got us off of the damn ground!
Byakugan is a in English "White Eye" giving the user the ability to see through solid matter (X-ray, Chakra Scope) in addition to this the byakugan can see the human body's vascular system or chakra network. These one hundred and twenty eight points swirling on the body are known as the chakra points. In combination with the hyuuga clan taijutsu and byakugan, this art "Juken" slams indirect shots using the eyes to see the points and sealing up chakra. On top of that, the byakugan spans to a diameter of from what neji has 859 meters also enabling them to track in the sense of 'detection' when movement is involved.
Don't confuse that last part with sharingan predicting movement.
Now for the sharingan.
It's a blood trait of the uchiha clan giving the user incredible and peak clarity of insight. The sharingan gives the user the ability to see the color of chakra, not only that but follow and anticipates it's flow as it enters the body. Using the "piercing eye" trait of the sharingan, the wielder is able to copy and reproduce physical actions at the very second their opponent does. When applying this combat, as chakra flow through out the entire body, a certain image is given off depicting their retaliation. This image is a glance of the opponents actions, making it seem as though a sharingan user can "see the future" when it's damn sure close to it. The second trait of the sharingan would be the special brand of hypnosis or "hypnotic eye" as it can cast genjutsu via a single glance. Kekkei genkai doujutsu cannot be broken, but resisted (As you've seen with one Akatsuki member >.>). Last but not least the ability to copy an opponents Jutsu with two exceptions to this,
Blood Contract Summons
Other Kekkei Genkai
As for the creation of the sharingan. It goes FAR BACK to the Great Sojobo, The Tengu Lord. It was said he fell in love with a woman by the house hyuuga and they conceived a child giving birth to a new breed of doujutu. The very first user of the sharingan...Madara Uchiha.
Thats about all I know on the subject.