Homocysteine is an amino acid found in the blood. It's a very important marker for long term health. Lets back step for a second. Methionine is an essential amino acid obtained from protein. Some methionine is turned into homocysteine. The body turns much of the homocysteine in the body back to methionine with the help of B12. If B12 is lacking the homocysteine levels gradually increase.
Homocysteine can be a nerve toxin promoting cardivascular disease, stroke and Alzheimer's. Keeping the homocysteine levels low is associated with lower disease rates, but this requires adequate levels of b12 and folate. For non vegetarians, folate is more important for keeping homocysteine levels down, for vegetarians B12 is more important. So if your non vegetarian a folate supplement is advised or eating a lot of foods such as beans, lentils, lettuce, black eyed peas, okra and banannas. If your a vegetarian it's advised to take a B12 supplement as it's hard to get the required amount of B12, there are fortified foods out there, but in reality it is advised to be on a B12 supplement for optimal health. Remember, optimal is what were after.