According to Ovidius, Pygmallion was a Cypriot sculptor, who fell in love with an ivory woman statue he carved. The goddess Aphrodite appreciated his love and offerings and changed the statue to a real woman. Pygmallion then married her and they had a daughter. So much for the history or mythology, now let's go back to management. The phenomenon called Pygmalion effect says that others' expectations from a person are affecting that person's performance.
Sometimes it is called also Rosenthal effect based on the study and experiment of Rosenthal and Jacobson, which has shown that the children's school performance can be influenced by teacher's expectations (for more of the study details check for example https://psych.wisc.edu/braun/281/Intelligence/LabellingEffects.htm ). Besides explanations via "esoteric" or quantum mechanics (e.g. the observer effect), the behavioral explanation of this effect says that our expectations/beliefs about others impact our actions towards them, which then impact their beliefs about themselves and finally their actions (towards us or in general). These actions then strenghten our beliefs about them and the circle of impacts continues to strenghten.
Based on the above, the leader's expectations from people or from team is affecting their actions and performance. Thus the positive expectations can be one of the means for performance improvement. It can be strenghtened further by giving emphasis to positive feedback and considering mistakes as areas for improvement (e.g. via coaching management style).