If a company chooses to pay a dividend, it will be divided proportionally based on the total number of shares that exist. If stock owners have voting rights in corporate affairs, the voting rights given to shareholders are typically dependent on the number of shares you own.
Taking the terminology a step further, a shareholder is an individual who owns shares of stock in a company. This term is often (correctly) used interchangeably with stockholder.
The value of a share of stock depends on several factors, such as the sales, growth, or profitability (or lack thereof) of the underlying business, as well as overall market factors such as the health of the economy, interest rate conditions, and more.
Public versus private companies
While the general idea is the same in regard to equity in a business, there are some stocks that trade on the public stock markets and some that don't.
Publicly traded stocks are the most visible. These are companies like Microsoft (MSFT +0.00%) and Coca-Cola (KO -1.23%) whose shares can be bought on major stock exchanges by anyone with a funded U.S. brokerage account. But it's important to understand that privately owned companies have shares of stock as well -- they are just not available for purchase by everyday investors. The process a private company uses to become a publicly traded company, and therefore allow its shares to be owned by everyday investors, is known as an initial public offering, or IPO.