A share is a single unit of ownership. A company divides its ownership into shares, and each one gives its holder a slice of the business, usually with a vote and a right to any dividends; together these shares are the company's stock, which is explained in full on that page. Funds also issue shares, whose price is the fund's net asset value per share.
A person who owns shares is a shareholder, and funds may sell several share classes with different fees.