Stock is the initial capital that a company starts with. Owners own a portion (and are therefore stockholders), which gives them fractional rights to company profits. When a company goes public, it splits stock into tiny fractions and sells them on the open market. The fractions are called shares and often represent one-millionths of ownership of company stock -- or less. People who own shares are also stockholders, or shareholders. When a company is private, a small group of stockholders own company equity whereas a large group owns company equity in public companies.
Equity appears on a company's balance sheet. The balance sheet is a statement of all assets (things of value that the company owns) and all liabilities (responsibilities that the company has to send money out) and unsurprisingly is divided into two parts: assets and liabilities. The balance sheet lists all types of assets and liabilities along with their values and totals in the first two sections. The balance sheet reports the difference in the totals as "shareholder equity" in the last section.
Any change in assets affects equity. Rises in sales, accounts receivable (money that the company is owed but has not received), property and equipment values, cash and cash equivalents, for example, increases shareholder equity, assuming that the liabilities remain constant. Any decreases -- defaults on accounts receivable, lower valuations for property -- lowers equity.
Liabilities refer to a company's financial responsibilities, and any change in liabilities also affects equity. Accounts payable, short-term and long-term debt, inventory costs and other line items affect shareholder equity. An increase in money owed to suppliers, interest rates or inventory costs causes total liabilities to rise and, if assets stay constant, decreases shareholder equity. Likewise, any decrease in the amount of money that a company needs to pay out increases shareholder equity.