What is the meaning of Efficient Frontier?

I have an assignment due next week. Can you elaborate the definition if Efficient Frontier?
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"The efficient frontier represents that set of portfolios with the maximum rate of return for every given level of risk, or the minimum risk for every level of return - Frontier will be portfolios of investments rather than individual securities: Exceptions being the asset with the highest return and the asset with the lowest risk - Any portfolio that lies on the upper part of the curve is efficient: it gives the maximum expected return for a given level of risk. - A rational investor will only ever hold a portfolio that lies somewhere on the efficient frontier. The maximum level of risk that the investor will take on determines the position of the portfolio on the line. Source:"
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"A set of best investment portfolios which offers the very best anticipated returning for a described higher level of peril or perhaps the most affordable chance for any presumption a higher level expected give back. Domain portfolios in which sit down below the useful frontier are sub-optimal, because they do not supply ample come back for your a higher level danger. Domain portfolios in which cluster to the right on the efficient frontier are sub-ideal, since they have a higher level connected with chance to the defined pace connected with returning. "
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