While warfarin is often referred to as a 'blood thinner', it doesn't actually make your blood thinner. Warfarin interferes with your body's ability to form a blood clot, so really should be referred to as an 'anti-clotting' medicine. Normally, the blood's ability to form a clot is helpful in preventing unwanted bleeding if you cut or injure yourself. In some people, the blood clots too easily because of illness. In these people, anti-clotting medications are required.
In order for your blood to form a clot, you have to have certain proteins in your blood called clotting factors. Normally, your liver makes these clotting substances and it requires vitamin K from the diet to do so. Warfarin reduces your liver's ability to use vitamin K to make these clotting factors, which makes it harder for your blood to clot.
Because everybody is different it makes sense that everybody reacts differently to warfarin. The effects of warfarin are very unpredictable from person to person. As no two people are the same you will probably find that your warfarin dose is likely to change often until your doctor finds the best dose for you. This often involves lots of blood tests to make sure that your warfarin is working the best it can for you.