Technically, vitamin K is a fat-soluble class of compounds that are involved in a unique biological reaction - the carboxylation (adding of a CO2) to glutamic acid residues of certain "vitamin K-dependent" proteins. (Glutamic acid is one of the amino acids in proteins.) Once these residues are carboxylated, they can bind to calcium, which they need to do in order to work properly.
The only undisputed function of these vitamin K-dependent proteins is to assist in the coagulation cascade. Clotting factors II, VII, IX and X (which promote clotting) and Protein S and Protein C (which both inhibit coagulation) are dependent on the above modification in order to become active.
Other vitamin K-dependent proteins have been discovered too. For instance, osteocalcin (in bones) and an extracellular matrix protein are both carboxylated with the help of the above vitamin. However, it is unclear what function they have.
After it's been used up in the above reaction, vitamin K is recycled by the body. Warfarin, a common anticoagulant used by us doctors, works by inhibiting this recycling process.