K-Stability is a concept in algebraic geometry that helps determine whether a given Fano variety can be considered stable. It involves analyzing the behavior of certain geometric objects under specific conditions, particularly focusing on the properties of their associated polarized varieties. In simpler terms, K-stability provides a way to assess if a variety can be deformed into a more desirable form while maintaining its essential characteristics. This concept is crucial for understanding the geometric structure and classification of varieties, especially in the context of moduli spaces and mirror symmetry.