The Betz limit is the theoretical maximum efficiency for a wind turbine, conjectured by German physicist Albert Betz in 1919. Betz concluded that this value is 59.3%, meaning that at most only 59.3% of the kinetic energy from wind can be used to spin the turbine and generate electricity. In reality, turbines cannot reach the Betz limit, and common efficiencies are in the 35-45% range.
Wind turbines work by slowing down passing wind in order to extract energy. If a wind turbine was 100% efficient, then all of the wind would have to stop completely upon contact with the turbine—which isn't possible by looking at a wind turbine (figure 1). In order to stop the wind completely, the air wouldn't move out of the way to the back of the turbine, which would prevent further air from coming in—causing the turbine to stop spinning.
For a slightly technical derivation of the Betz efficiency limit, click here.