Equities are the same as shares of a commercial company. Company shares simply represent the ownership of that company i.e. the company is owned by the shareholders.
Thus the terms equity market and stockmarket are interchangeable and simply mean the market where equities in different companies are bought and sold.
Equity holders, as owners of the company are generally entitled to a share of the profits. These may be paid to them in the form of dividends. A dividend is just the name for the payment received by a shareholder from the company representing a part of the profits made by the company. The exact dividend to be paid is determined by the board of directors.
Equities in large companies are often traded on the stockmarket. Such companies are called public companies. The share price is therefore a representation of the value of the company i.e. the market capitalisation of a company is just the number of shares it has in issue multiplied by the share price.
In order to measure the performance of the market as a whole, or of different types of companies with it, stockmarket indices have been developed as a way of tracking the value of groups of companies.
The FTSE-100 index for example measures the share prices of the 100 largest companies listed on the London stockmarket. Note that the measure of size is market capitalisation and not for example profits or revenue.