Equity is the stake its owners have in a company. The word can be used to refer to balance sheet quantities, or as an adjective to describe securities that give their holders a share of ownership of the issuer.
On a balance sheet, the equity is the amount that belongs to the shareholders; a company's assets less its liabilities.
Equity one of the two main sources of funding for companies, the other being debt.
Companies raise equity capital by issuing equity securities. This is most commonly in the form of ordinary shares. Ordinary shares usually have equal voting rights to all other ordinary shares (one share, one vote), and are entitled to equal dividends.
The other common type of shares are preference shares, which have some characteristics that make them more akin to bonds, although they are legally (and therefore for tax purposes) shares.
Some companies may have special classes of shares that have more rights than ordinary shares. This has become uncommon. Golden shares and founders' shares still sometimes exist for particular purposes.
Some companies also have classes of share that have fewer rights than ordinary shares, most commonly non-voting shares, but there are also various types of deferred shares. These are typically entitled to the same share of profits as ordinary shares, but do not give the shareholder who holds one any voting rights. Again, these are becoming less common.
Investors are generally (quite rightly) very wary of companies that voting rights structured to distribute control differently from economic interests in the company. This usually means that a particular group of shareholders can run the company (or very strongly influence its running) to suit themselves.
A company's articles define the rights of different classes of shareholders and endless variations on the above are possible. Changes to the rights of different classes of shareholders usually require the agreement of the majority of shareholders of each class of shares affected, even if these are non-voting shares.