An efficient portfolio is one that lies on the efficient frontier.
An efficient portfolio provides the lowest level of risk possible for a given level of expected return. If a portfolio is efficient, then it is not possible to construct a portfolio with the same, or a better level, of expected return and a lower volatility.
An efficient portfolio also provides the best returns achievable for a given level of risk. If a portfolio is efficient it is not possible to construct a portfolio with a higher expected return and the same or a lower level of volatility with the securities available in the market, excluding risk free assets. Adding the latter allows one to construct portfolios that lie on the securities market line.
The market portfolio is an efficient portfolio, and its risk and returns are those of the point where the securities market line touches the efficient frontier.