Common stock is a form of corporate equity ownership, a type of security. The terms voting share and ordinary share are also used frequently in other parts of the world; "common stock" being primarily used in the United States. They are known as equity shares or ordinary shares in the UK and other Commonwealth realms. This type of share gives the stockholder the right to share in the profits of the company, and to vote on matters of corporate policy and the composition of the members of the board of directors.
The term "common stock" indicates that the investors in the company do not own any particular assets, but that instead all of the assets are the shared, or common, property of all investors. A corporation may issue both common and preferred stock, in which case the preferred stockholders have priority to receive dividends. In the event of liquidation, common stock investors receive any remaining funds after bondholders, creditors (including employees), and preferred stockholders are paid. When the liquidation happens through bankruptcy, the common stock investors typically receive nothing.
Since common stock is more exposed to the risks of the business than bonds or preferred stock, it offers a greater potential for capital appreciation. Over the long term, common stocks tend to outperform more secure investments, despite their short-term volatility.
Shareholder rights are more conceptual than technical or factual. Their most common source is in the statutory and case law of the jurisdiction in which the company was formed. Information about what people think of as shareholder rights can also be found in the corporate charter and governance documents, but companies do not actually have documentation outlining specific "Shareholder Rights". Some shareholders elect to enter into shareholder agreements that create new rights among the shareholders, and it is common for the company to be a party to that agreement.
Some common stock shares have voting rights on certain matters, such as electing the board of directors. However, in the United States, a company can have both a "voting" and "non-voting" series of common stock, as with preferred stock, but not in countries which have laws against multiple voting and non-voting shares.
Hypothetically speaking, holders of voting common stock can influence the corporation through votes on establishing corporate objectives and policy, stock splits, and electing the company's board of directors. In practice, it's questionable whether or not such actions can be organized or ruled in their favor. Some shareholders, including holders of common stock, also receive preemptive rights, which enable them to retain their proportional ownership in a company if it issues additional stock or other securities. There is no fixed dividend paid out to common/equity stockholders and so their returns are uncertain, contingent on earnings, company reinvestment, and efficiency of the market to value and sell stock. 
Common/Equity stock is classified to differentiate it from preferred stock. Each is considered a stock class, with different series of each issued from time to time such as Series B Preferred Stock. Nevertheless, using "Class B Common Stock" is a common label for a super-voting series of common stock.