The ability of an economic agent (firm or consumer) to affect the equilibrium price in a market. Market power derives from being large relative to the market, so the N-firm concentration ratio is often used as a proxy. A monopoly supplier of a product has market power: they can set the price that maximizes profit. Similar considerations apply to market power on the demand side of the market. There are several determinants of market power in addition to size. These include barriers to entry, brand recognition, and product differentiation.
Reference: Oxford Press Dictonary of Economics, 5th edt.