Equity is the risk-bearing part of a company's capital, usually referred to as ordinary shares. The owners of the equity, the shareholders, are the owners of the company and have the right to elect directors and share in the company's profits through the payment of dividends.
There are other broader meanings to the word 'equity'. It can also refer to the value of securities over the debit balance in a margin account.
Equity has a slightly different meaning when it comes to home ownership!