Plot every possible combination of assets with expected return on the vertical axis and volatility on the horizontal. The upper-left boundary of the resulting cloud is the efficient frontier. A portfolio expected to return 6% at 12% volatility is inefficient if another mix returns 7% at the same 12%.
The curve exists because of imperfect correlation. Two assets each at 15% volatility with a correlation of 0.3 combine 50/50 into a portfolio with volatility of about 12.1%, lower than either component. That reduction is what bends the frontier upward and left.
The practical warning is that the frontier is drawn from estimates. Shift an expected return input by one percentage point and the "optimal" portfolio can change completely, which is why frontier output should be treated as a rough map rather than a instruction. See mean-variance-optimization.
Related: modern-portfolio-theory, mean-variance-optimization, correlation, sharpe-ratio, asset-allocation