The Cost of Capital is the hurdle over which a business must get to generate positive cash flow. It is what it will cost companies to get capital from investors.
Companies sometimes use debts or equities to finance their business operations. The service paid on debt and the operating expenses are lines over which the revenue must get to be saved as retained earnings or distributed as dividends. The yield expected by investors on debt is the cost of capital for the company taking on those loans.
This is called cost of debt and is easy to understand. The return expected by equity investors is a slipperier number, which is often arrived at using the Capital Asset Pricing Model, which takes Beta and the current risk-free rate into account. What dividend will those investors expect for taking on the risk of investing capital into this business? This is called Cost of Equity.
When both are used, a weighted average must be useful, which would be the Weighted Average Cost of Capital (WACC). The board members of a company might make a decision on whether or not to raise capital to start a new project by looking at the cost of capital in the current environment.