A company can be defined as an artificial legal person, which implies that a company can make contracts and take legal action against others and others also can take legal action against the company. It is an entity which is distinct from its members. Companies falls into two categories it may either a public or private company.
A public company is one which has sold its shares to public through initial public offering and public companies have to follow strict rules and regulation as set by the exchanges on which the company is listed. Public company has many shareholders and therefore they should have board of directors and they must report financial information every quarter. Public companies can raise funds for expansion from capital markets by making follow on public offer as they are already listed in stock market.
A privately held company is one whose shares are held by one shareholder who is the owner of a company or a small group of shareholders. Shares of private companies are not bought and sold in stock markets and also private companies are not bounded by the rules and regulations of the stock market, they are also not obliged to publish there results every quarter unlike public companies which have to publish results every quarter to their investors.