A company whose common shares are owned by one individual owner or by a small group of controlling stockholders. This is in contrast to a widely held stock, in which thousands or even millions of different investors may own shares in a large company.
Taobiz explains Closely Held Stock
Closely held stock is typically not publicly traded on exchanges because the small number of owners rarely sell their shares. A common way that a closely held stock is created is when an entrepreneur starts and incorporates his or her own business, but retains ownership of all the company's outstanding shares.