There are a number of possible answers to your question, but first it is important to know how hair color is generated. 

Your hair is primarily composed of the protein keratin. 

Keratin, like all proteins is colorless -- those proteins that have a color, such as the hemoglobin that gives your blood its red color, get their color from associated pigments. 

The pigments responsible for hair color are variants of the molecule melanin. 

The cells that make melanin are known as melanocytes ('cytes' means cells). 

All melanocytes are derived from a structure that forms early during embryonic development, the neural crest.

Neural crest cells migrate away from the neural tube (where they form) and go on to generate large parts of your face and peripheral nervous system. 

Some neural crest differentiate into melanoblasts (a 'blast' is a dividing cell).  Melanoblasts are the stem cells that divide to produce melanocytes.  

Melanocytes are 'dendritic' or tree-like in shape.  

This is a photograph of melanocytes in the skin of frog tadpole -- you can see the melanocytes because their cytoplasm is filled with melanin particles. 

The melanocytes are surrounded by cells that do not contain melanin and so are invisible in this photograph.

Melanocytes pass pigment to surrounding cells through a process known as phagocytosis.  Basically, neighboring cells eat (phago) parts of the melanocyte. 

Since melanin is difficult to digest, it persists in the cells that ingest it, giving them a color. 

The exact color is dependent upon the type of melanin-like molecule made by the melanocytes and the amount of ingested by the neighboring cells. 

The more melanin a cell ingests from neighboring melanocytes, the darker it becomes. 

This same process is used to generate hair color -- the keratinocytes that form the hair shaft pick up melanin from melanocytes in the hair follicle. 

So, finally to the answer to your question.  How can I have a patch of white, that is unpigmented, hair? 

Technically, this condition is known as poliosis (from polios meaning gray) and is related to a more general condition called vitiligo (or leukodermia - which means white skin), in which patches of unpigmented skin appear.

Now that your know how hair gets its color, you should be able to make the connection between poliosis and vitiligo.  If melanocytes disappear from an area of skin, the skin and the hairs that grow out from it will be unpigmented -- that is, white. 

So what can make this happen?  The answer is not conclusively known, but likely to involve what is known as an auto-immune disorder. 

Basically, what it thought to happen is that your immune system, which normally fights off external parasites and pathogens (viruses and bacteria), makes a mistake and attacks some of your own normal cells. 

If your immune system kills the melanocytes in a region of the skin (or they die for some other reason), the supply of pigment will disappear and the skin will become unpigmented. 

Remember, melanocytes are derived from melanoblasts that migrated to the skin during embryonic development.

If the autoimmune response kills melanocytes, but leave melanoblasts -- the skin could become repigmented.  If the melanoblasts are killed, it will remain unpigmented. 

The condition is in itself not dangerous, but it can be a sign of a susceptibility to other auto-immune diseases. 

You should watch your immune system carefully by routine visits to a physician.  If a more dangerous condition were to appear you could treat it early.