Financial terms can be confusing. "Common stock equity" is one such term. "Common" stock refers specifically to a share of stock that is distinct from "preferred" stock (another type of investment offering). However, both common and preferred stock are considered "equity shares"---that is, a share of stock in a company.
The purpose of issuing common stock is to raise capital for investment and growth
Equity Share
An "equity share" is another term for what most people simply call stock. Stocks in a company represent partial ownership, and since all stocks represent the same amount of ownership, they can be referred to as equity shares. Equity refers specifically to the value of these shares, not the shares themselves: equity could be negative if the liabilities on an asset (like a share of stock) outweigh the value of the asset. Equity is a very general word, used for many applications in finance and accounting.
Common Stock
Common stock is a specific form of equity ownership in a firm; it is called "common" to distinguish it from "preferred" stock holdings. Theoretically, the preferred stock is a superior instrument to the common stock, as the terms on preferred stocks can be negotiated with the firm. Further, preferred stocks may have priority over common stock in dividends and in asset liquidation proceedings. Common stocks, however, generally perform better than preferred stocks in the long run and also come with corporate voting rights (unlike preferred stocks).
Function
Common stock equity is designed to raise funds for investment for the issuing firm. When a firm issues common stock for the first time, the firm has what is called an initial public offering (often shortened to IPO). The IPO is an investment move by a firm, because in return for selling away ownership shares in the firm (equity shares), the firm receives capital. This capital is entered into the books as "shareholders' equity" or some variation on that term, such as "stockholders' equity" or "shareholders' capital."
Accounting for Equity
When firms issue equity, either in the form of common stock or in the form of preferred stock, the revenues from these issues are reported on the balance sheet. The balance sheet is a mandatory Securities and Exchange Commission (SEC) filing for American firms, and lists the assets and liabilities for the firm. Balance sheets and other financial documents for firms can be obtained from many corporate websites or from the SEC website. Using the balance sheet, an interested investor can see exactly how much preferred stock and common stock has been issued by that firm.
Significance
Common stock equity and other forms of joint equity has been a major source of economic growth for much of the modern economic period. Joint-stock firms arose during the age of exploration, as a way to share risks among many owners. Firms like the Virginia Company and the East India Company were among the first joint-stock firms, and shares were traded on the Amsterdam Stock Exchange as early as 1602. Common stock enables capital accumulation and risk-sharing, both essential characteristics of modern market economies.