Vitamin K is a series of compounds present in plants and animals, although they have totally different roles in the two kingdoms. Vitamin K was discovered by German researchers in the 1930s, who fed chicks a diet purified of fat, and discovered that the chicks developed problems with bleeding. From this they were led to discover a fat soluble vitamin that had coagulation properties (or "koagulation" in German) from which came the name Vitamin K.
Is the basic structure of the Vitamin K's. The side chain varies mostly in the length of which the basic unit, a straight double bonded carbon chain
repeats. The length of the side chain is mostly irrelevant for the compounds action in humans.
The importance of Vitamin K in plants is it is one of the many chemicals involved in the process of electron transport, and can often be found very close to the Clorophyll molecule. In plants, the sidechain is a phytol group, and this is the same phytol group that is present in Clorophyll. Also, in plants, the sidechain is actually the active party, while the ring group is incidental.
In animals, however, it is quite the opposite, with the sidechain being incidental, and the active group being the ring system. The action of the ring system is quite complicated, with one of the double bonded oxygen molecules oxidizing a single amino acid residue that then causes proteins to change their electrostatical configuration, etc., which seems slight, but it is what stops (most of) us from not bleeding to death over a paper cut.
In addition to its role in blood clotting, the Vitamin K's also play a significant but poorly understood role in ossification, with babies born to women who were using warfarin (an anti-clotting agent) showing a variety of bone malformations of varying degrees. This comes about because the same protein used in clotting is activated by Vitamin K for calcium fixing.
All of this being said, most people do not have to worry about their Vitamin K intake, since it is present both in all green vegetables, and is synthesized by bacteria in the intestine.