Equity investment refers to buying a piece of a company. You do this by buying shares in that company. There are two ways to acquire shares in a company: from the primary market, where you buy a company's share when it first issues shares (or equity). This first share offering is called an initial public offering (IPO). Or, you could buy equity in the secondary market, which is the stock exchange.
When you buy or sell equity on a stock exchange, you have to do the transaction through an exchange-certified broker/brokerage firm, who will now act as your agent whenever you want to buy or sell equity.
Equity investments are high-risk high-return propositions. There is scope for serious erosion of capital as well as considerable appreciation. This depends on many factors such as performance of the company, general market conditions, state of the economy and so on...
In an investment portfolio, the equity portion represents one end of the risk-return spectrum, the high end. No other investment tool gives you this much scope for capital appreciation.