Equity/share/stock is a type of security that is issued by companies to raise capital in exchange for part-ownership interest in that company.
If you own equity in a company, it refers to the fact that you have part-ownership interest in that company, and that entitles you to the residual assets (dividend and or bonuses) after clearing of all debt and tax obligations.
Equities are traded for the purpose of either capital gain/appreciation or dividend income as return on investment or both.