K-stable refers to a property in mathematics, particularly in the field of algebraic geometry and the study of moduli spaces. A variety is considered K-stable if it satisfies certain conditions related to its Kähler metrics and Fano varieties. This stability is crucial for understanding the geometric structure and behavior of these varieties. In practical terms, K-stability helps in classifying algebraic varieties and plays a significant role in the Yau-Tian-Donaldson conjecture. This conjecture connects K-stability with the existence of Kähler-Einstein metrics, which are important for various applications in both mathematics and theoretical physics.